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13.5: Exercises - Mathematics


1. List out the elements of the set “The letters of the word Mississipi”

2. List out the elements of the set “Months of the year”

3. Write a verbal description of the set ({3,6,9})

4. Write a verbal description of the set ({a, i, e, 0, u})

5. Is {1,3,5} a subset of the set of odd integers?

6. Is ({A, B, C})a subset of the set of letters of the alphabet?

For problems 7-12, consider the sets below, and indicate if each statement is true or false.

(A={1,2,3,4,5} quad B={1,3,5} quad C={4,6} quad U={ ext { numbers from } 0 ext { to } 10})

7. (3 in B)

8. (5 in C)

9. (B subset A)

10. (C subset A)

11. (C subset B)

12. (C subset U)

Using the sets from above, and treating (U) as the Universal set, find each of the following:

13. (A cup B)

14. (A cup C)

15. (A cap C)

16. (B cap C)

17. (A^{c})

18. (B^{c})

Let (D={b, a, c, k}, quad E={t, a, s, k}, quad F={b, a, t, h}). Using these sets, find the following:

19. (D^{c} cap E)

20. (F^{c} cap D)

21. ((D cap E) cup F)

22. (D cap(E cup P))

23. ((F cap E)^{c} cap D)

24. ((D cup E)^{c} cap F)

Create a Venn diagram to illustrate each of the following:

25. ((F cap E) cup D)

26. ((D cup E)^{c} cap F)

27. (left(F^{c} cap E^{prime} ight) cap D)

28. ((D cup E) cup F)

Write an expression for the shaded region.

29.

30.

31.

32.

Let (A={1,2,3,4,5} quad B={1,3,5} quad C={4,6}). Find the cardinality of the given set.

33. (mathrm{n}(A))

34. (mathrm{n}(B))

35. (mathrm{n}(A cup C))

36. (mathrm{n}(A cap C))

The Venn diagram here shows the cardinality of each set. Use this in 37-40 to find the cardinality of given set.

37. (mathrm{n}(A cap C))

38. (mathrm{n}(B cup C))

39. (mathrm{n}left(A cap B cap C^{2} ight))

40. (mathrm{n}left(A cap B^{c} cap C ight))

41. If (n(G)=20, n(H)=30, n(G cap H)=5,) find (n(G cup H))

42. If (n(G)=5, n(H)=8, n(G cap H)=4,) find (n(G cup H))

43. A survey was given asking whether they watch movies at home from Netflix, Redbox, or a video store. Use the results to determine how many people use Redbox.

(egin{array}{ll} ext{52 only use Netflix} & ext{62 only use Redbox} ext{24 only use a video store} & ext{16 use only a video store and Redbox} ext{48 use only Netflix and Redbox} & ext{30 use only a video store and Netflix} ext{10 use all three} & ext{25 use none of these} end{array})

44. A survey asked buyers whether color, size, or brand influenced their choice of cell phone. The results are below. How many people were influenced by brand?

(egin{array}{ll} ext{5 only said color} & ext{8 only said size} ext{16 only said brand} & ext{20 said only color and size} ext{42 said only color and brand} & ext{53 said only size and brand} ext{102 said all three} & ext{20 said none of these} end{array})

45. Use the given information to complete a Venn diagram, then determine: a) how many students have seen exactly one of these movies, and b) how many had seen only Star Wars.

(egin{array}{ll} ext{18 had seen The Matrix (M)} & ext{24 had seen Star Wars (SW)} ext{20 had seen Lord of the Rings (LotR)} & ext{10 had seen M and SW} ext{14 had seen LotR and SW } & ext{12 had seen M and LotR} ext{6 had seen all three} & ext{} end{array})

46. A survey asked people what alternative transportation modes they use. Using the data to complete a Venn diagram, then determine: a) what percent of people only ride the bus, and b) how many people don’t use any alternate transportation.

(egin{array}{ll} ext{30% use the bus} & ext{20% ride a bicycle} ext{25% walk} & ext{5% use the bus and ride a bicycle} ext{10% ride a bicycle and walk} & ext{12% use the bus and walk} ext{2% use all three} & ext{} end{array})


NCERT Solutions for Class 12 Maths Chapter 13 Probability Ex 13.5

The topics and sub-topics included in Chapter 13 Probability the following:

Section Name Topic Name
13 Probability
13.1 Introduction
13.2 Conditional Probability
13.3 Multiplication Theorem on Probability
13.4 Independent Events
13.5 Bayes’ Theorem
13.6 Random Variables and its Probability Distributions
13.7 Bernoulli Trials and Binomial Distribution

NCERT Solutions for Class 12 Maths Chapter 13 Probability 13.5 are part of NCERT Solutions for Class 12 Maths. Here we have given Class 12 Maths NCERT Solutions Probability Ex 13.5

Class 12 Maths Probability Solutions

Question 1.
A die is thrown 6 times. If ‘getting an odd number’ is a success, what is the probability of
(i) 5 successes?
(ii) at least 5 successes?
(iii) at most 5 successes?
Solution:

Question 2.
There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item ?
Solution:

Question 3.
A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability, of two successes.
Solution:

Question 4.
Five cards are drawn successively with replacement from a well- shuffled deck of 52 cards. What is the probability that
(i) all the five cards are spades?
(ii) only 3 cards are spades?
(iii) none is spade?
Solution:

Question 5.
The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs.
(i) none
(ii) not more than one
(iii) more than one
(iv) at least one will fuse after 150 days of use
Solution:

Question 6.
A bag consists of 10 balls each marked with one of the digits 0 to 9. If four bails are drawn successively with replacement from the bag, what is the probability that none is marked with the digit 0?
Solution:

Question 7.
In an examination, 20 questions of true – false type are asked. Suppose a student tosses fair coin to determine his answer to each question. If the coin falls heads, he answers ‘true,’ if it falls tails, he answers “ false’. Find the probability that he answers at least 12 questions correctly.
Solution:

Question 8
Suppose X has a binomial distribution (Bleft( 6,frac < 1 > < 2 > ight) ). Show that X = 3 is the most likely outcome.
(Hint: P (X = 3) is the maximum among all P (Xi), xi. = 0,1,2,3,4,5,6)
Solution:

Question 9.
On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?
Solution:

Question 10.
A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is (frac < 1 >< 100 >) . What is the probability that he will win a prize?
(a) at least once,
(b) exactly once,
(c) at least twice?
Solution:

Question 11.
Find the probability of getting 5 exactly twice in 7 throws of a die.
Solution:

Question 12.
Find the probability of throwing at most 2 sixes in 6 throws of a single die.
Solution:

Question 13.
It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles 9 are defective?
Solution:

Question 14.
In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is
(a) (< 10 >^< -1 >)
(b) (< left( frac < 1 > < 2 > ight) >^< 5 >)
(c) (< left( frac < 9 > < 10 > ight) >^< 5 >)
(d) (frac < 9 >< 10 >)
Solution:

Question 15.
The probability that a student is not a swimmer is (frac < 1 >< 5 >). Then the probability that out of five students, four are swimmers is:

Solution:

Class 12 Maths NCERT Solutions

  • Chapter 1 Relations and Functions
  • Chapter 2 Inverse Trigonometric Functions
  • Chapter 3 Matrices
  • Chapter 4 Determinants
  • Chapter 5 Continuity and Differentiability
  • Chapter 6 Application of Derivatives
  • Chapter 7 Integrals Ex 7.1
  • Chapter 8 Application of Integrals
  • Chapter 9 Differential Equations
  • Chapter 10 Vector Algebra
  • Chapter 11 Three Dimensional Geometry
  • Chapter 12 Linear Programming
  • Chapter 13 Probability Ex 13.1

We hope the given NCERT Solutions for Class 12 Maths Chapter 13 Probability Exercise 13.5 will help you. If you have any query regarding Class 12 Maths NCERT Solutions Probability Ex 13.5, drop a comment below and we will get back to you at the earliest.


Download Free PDF for NCERT Solutions Class 12 Maths Chapter 13 Exercise 13.5

Bernoulli trials: Bernoulli trials of a random experiment are called Bernoulli Trials. However, this experiment need to satisfy these conditions:-

  • There should be a finite number of trials.
  • The trials should be independent.
  • Each trial has exactly two outcomes such as success or failure
  • The probability of success remains the same in each trial.

Each trial has effects heads (fulfillment) and tails (failure). The chance of fulfillment on every trial is p = half and the chance of failure is q = 1 − half=half. We are interested in the variable X which counts the wide variety of successes in 12 trials. This is an instance of a Bernoulli Experiment with 12 trials.

Binomial distribution: The binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, either success or failure.

The residences of the binomial distribution are: There are feasible outcomes: genuine or false, fulfillment or failure, sure or no. There is ‘n’ variety of impartial trials or a hard and fast variety of n instances repeated trials. The possibility of fulfillment or failure varies for every trial. Only the variety of fulfillment is calculated out of n impartial trials. Every trial is an impartial trial, this means that the final results of 1 trial do now no longer affect the final results of every other trial.


Surface Areas and Volumes : Exercise 13.5 (Mathematics NCERT Class 9th)

Here, l = 8 m, b = 6 m and h = 3 m
Volume of the pit
=
Rate of digging is Rs 30 per
Therefore Cost of digging the pit = Rs (144 × 30) = Rs 4320.

Q.5 The capacity of a cuboidal tank is 50000 litres of water. Find the breadth of the tank, if its length and depth are respectively 2.5 m and 10 m.
Sol.

Here, length = 2.5 m, depth = 10 m and volume = 50000 litres


Q.6 A village having a population of 4000, requires 150 litres of water per head per day. It has a tank measuring 20 m × 15 m ×6 m . For how many days will the water of this tank last?
Sol.

Here , l = 20 m , b = 15 m and h = 6 m
Therefore Capacity of the tank

Water requirement per person per day
Water required for 4000 person per day

Number of days the water will last

Thus, the water will last for 30 days.

Q.7 A godown measures 60 m × 25 m × 10 m. Find the maximum number of wooden crates each measuring 1.5 m × 1.25 m × 0.5 m that can be stored in the godown.
Sol.

Volume of the godown
Volume of 1 crates
Number of crates that can be stored in the godown

Q.8 A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.
Sol.

Let be volume of the cube of edge 12 cm . So , length = breadth = height = 12 cm
Volume of the cube
and = Volume of the cube cut out of the first one


Therefore , side of the new cube = 6 cm
Ratio of their surface areas

Q.9 A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?
Sol.

Since the water flows at the rate of 2 km per hour, the water from 2 km of river flows into the sea in one hour.
Therefore The volume of water flowing into the sea in one hour = Volume of the cuboid


Therefore , the volume of water flowing into the sea in one minute


Download Free PDF for NCERT Solutions Class 12 Maths Chapter 13 Exercise 13.2

As the two events such that the probability of occurrence of one of them is not affected by the occurrence of the other are called independent events.

Theorem: If A and B are two independent events, the probability that both will occur is equal to the product of their probabilities.

Let E and D be two events associated with a sample of an experiment. Then,
P(E ∩ F) = P(E) P(F|E), P(E) ≠ 0
= P(F) P(E|F), P(F) ≠ 0

If E, F, and G are three events associated with a sample space, then
P(E∩F∩G) = P(E) P(F|E) P(G|E∩F)

Independent Events:

Let E and F be two events associated with a sample space S. If the probability of occurrence of one of them is not affected by the occurrence of the other, then we say the two events are independent.

An independent event is an event that has no connection to another event’s chances of happening or not happening.

In other words, the event does not affect the probability of another event occurring.
Independent events in probability are no different from independent events in real life.

This event is not affected by the other events.

Example: Tossing a coin. Heads or tails are not affected by previous tosses.


Ex 13.5 Class 12 Maths Question 1.
A die is thrown 6 times. If ‘getting an odd number’ is a success, what is the probability of
(i) 5 successes?
(ii) at least 5 successes?
(iii) at most 5 successes?
Solution:
There are 3 odd numbers on a die
∴ Probability of getting an odd number on a die = =

Ex 13.5 Class 12 Maths Question 2.
There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item ?
Solution:
Probability of getting one defective item = 5%
=
=
Probability of getting a good item = =
A sample of 10 item include not more than one defective item.
=> sample contains at most (me defective item Its probability = P (0) + P (1)

Ex 13.5 Class 12 Maths Question 3.
A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability, of two successes.
Solution:
n(S) = 36, A = <11,22,33,44,55,66>

Ex 13.5 Class 12 Maths Question 4.
Five cards are drawn successively with replacement from a well- shuffled deck of 52 cards. What is the probability that
(i) all the five cards are spades?
(ii) only 3 cards are spades?
(iii) none is spade?
Solution:
S = <52 cards>, n (S) = 52
Let A denotes the favourable events
A= <13 spade>, n(A)= 13

Ex 13.5 Class 12 Maths Question 5.
The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs.
(i) none
(ii) not more than one
(iii) more than one
(iv) at least one will fuse after 150 days of use
Solution:
Probability that a bulb gets fuse after 150 days of its use = 0.05
Probability that the bulb will not fuse after 150 days of its use = 1 – 0.05 = 0.95
(i) Probability that no bulb will fuse after 150

Ex 13.5 Class 12 Maths Question 6.
A bag consists of 10 balls each marked with one of the digits 0 to 9. If four bails are drawn successively with replacement from the bag, what is the probability that none is marked with the digit 0?
Solution:
S = <0,1,2,3,4,5,6,7,8,9>,n(S) = 10
Let A represents that the ball is marked with the digit 0.
A = <0>, n(A) = 1

Ex 13.5 Class 12 Maths Question 7.
In an examination, 20 questions of true – false type are asked. Suppose a student tosses fair coin to determine his answer to each question. If the coin falls heads, he answers ‘true,’ if it falls tails, he answers “ false’. Find the probability that he answers at least 12 questions correctly.
Solution:
Probability that student answers a question true =
i.e., when a coin is thrown, probability that a head is obtained =
Probability that his answer is false = =
Probability that his answer at least 12 questions correctly = P (12) + P (13) + P (14) +…….. P (20)

Ex 13.5 Class 12 Maths Question 8
Suppose X has a binomial distribution . Show that X = 3 is the most likely outcome.
(Hint: P (X = 3) is the maximum among all P (Xi), xi. = 0,1,2,3,4,5,6)
Solution:


Ex 13.5 Class 12 Maths Question 9.
On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?
Solution:
P = . q = 1 – P = =

Ex 13.5 Class 12 Maths Question 10.
A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is . What is the probability that he will win a prize?
(a) at least once,
(b) exactly once,
(c) at least twice?
Solution:
Probability that the person wins the prize =
Probability of losing = =
(a) Probability that he loses in all the loteries

Ex 13.5 Class 12 Maths Question 11.
Find the probability of getting 5 exactly twice in 7 throws of a die.
Solution:
S = <1,2,3,4,5,6>,n(S) = 6
A = <5>=> n(A) = 1

Ex 13.5 Class 12 Maths Question 12.
Find the probability of throwing at most 2 sixes in 6 throws of a single die.
Solution:
When a die is thrown,
Probabiltiy of getting a six =
Probabiltiy of not getting a six = =
Probabiltiy of getting at most 2 sixes in 6 throws of a single die = P (0) + P (1) + P (2)

Ex 13.5 Class 12 Maths Question 13.
It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles 9 are defective?
Solution:
p = =
q = 1 – p = =

Ex 13.5 Class 12 Maths Question 14.
In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is
(a)
(b)
(c)
(d)
Solution:
p =
q = n = 5, r = 0, P(X=0) =
Option (c) is correct

Ex 13.5 Class 12 Maths Question 15.
The probability that a student is not a swimmer is . Then the probability that out of five students, four are swimmers is:

Solution:
p = , q = , n = 5,r = 4


Option (a) is true

We hope the NCERT Solutions for Class 12 Maths Chapter 13 Probability Ex 13.5 help you. If you have any query regarding NCERT Solutions for Class 12 Maths Chapter 13 Probability Ex 13.5, drop a comment below and we will get back to you at the earliest.


13.5: Exercises - Mathematics

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NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.5

Question 1.
A matchbox measures 4 cm x 2.5 cm x 1.5 cm. What will be the volume of a packet containing 12 such boxes?
Solution:
Volume of a match box = 4 cm x 2.5 cm x 1.5 cm= 15 cm 3
Volume of a packet = 12 x 15 cm 3 = 180 cm 3

Question 2.
A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many litres of water can it hold? ( 1 m 3 = 1000L)
Solution:
Volume of a cuboidal water tank = 6 m x 5 m x 4.5 m
= 30 x 4.5 m 3 = 135 m 3
= 135 x 1000L = 135000L (∵ 1 m 3 = 1000L)

Question 3.
A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?
Solution:
Volume of a cuboidal vessel = hold liquid
∴ l x b x h = 380 m3
⇒ 10 x 8 x h = 380
⇒ h = (frac < 380 >< 80 >)
⇒ h= 4.75m
Hence, the cuboidal vessel must be made 4.75 m high.

Question 4.
Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of ₹30 per m3.
Solution:
Volume of a cuboidal pit = l x bx h= (8 x 6 x 3)m 3 =144 m 3
∵ Cost of digging per m 3 = ₹ 30
∴ Cost of digging 144m 3 = ₹ 30x 144 = ₹ 4320

Question 5.
The capacity of a cuboidal tank is 50000 litres of water. Find the breadth of the tank, if its length and depth are 2.5 m and 10 m, respectively.
Solution:
Given, l = 2.5 m and h = 10m
Let breadth of tank be b.

Hence, breadth of the cuboidal tank is 2 m.

Question 6.
A village, having a population of 4000, requires 150 litres of water per head per day. It has a tank measuring 20 m x 15 m x 6 m. For how many days will the water of this tank last?
Solution:

Question 7.
A go down measures 40 m x 25 m x 10 m. Find the maximum number of wooden crates each measuring 15 m x 125 m x 0.5 m that can be stored in the go down.
Solution:
Dimension for godown, l = 40m b = 25 m and c = 10 m
Volume of the godown = l x b x h= 40 m x 25 m x 10 m
Dimension for wooden gate l = 1.5 m, b = 1.25 m, b = 1.25 m, h = 0.5 m
Volume of wooden gates = l x b x h = 1.5 m x 1.25 m x 0.5m

Question 8.
A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.
Solution:
Volume of a solid cube = 12 cm x 12 cm x 12 cm = 1728 cm 3
The solid cube is cut into eight cubes of equal volume.

Question 9.
A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?
Solution:
Given, l = 2 km= 2 x 1000 m = 2000m
b = 40 m
and h = 3 m
Since, the water flows at the rate of 2 km h -1 ,
i.e., the water from 2 km of river flows into the sea in one hour.
The volume of water flowing into the sea in one hour = Volume of the cuboid
= l x b x h
= (2000 x 40 x 3) m 3
= 240000 m 3
∴ The volume of water flowing into the sea in one minute
= (frac < 240000 >< 60 >) m 3
= 4000 m 3

We hope the NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.5 help you. If you have any query regarding NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.5, drop a comment below and we will get back to you at the earliest.


Ex 13.5 Class 9 Maths Question 1.
A matchbox measures 4 cm x 2.5 cm x 1.5 cm. What will be the volume of a packet containing 12 such boxes?
Solution.
Given, dimensions of match box = 4 cm x 2.5 cm x 1.5 cm
So, length (l) = 4 cm, breadth (b) = 2.5 cm and height (h) = 1.5 cm
∴ Volume of a match box = Volume of a cuboid (V)
= 4 cm x 2.5 cm x 1.5 cm
= 15 cm 3 [∵ volume of cuboid (V) = Ibh]
Volume of a packet containing 12 such boxes
= 12 x Volume of one match box = 12 x 15 = 180 cm 3

Ex 13.5 Class 9 Maths Question 2.
A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many liters of water can it hold?
(1m 3 = 1000 l)
Solution.
Given, length (l) = 6 m, breadth (b) = 5m and depth or height (b) = 4.5m Volume of a cuboidal water tank = 6 m x 5 m x 4.5 m [∵ volume of cuboid (V) = Ibh]
= 30 x 4.5m 3 = 135m 3
= 135 x 1000 L = 135000 L [∵ 1 m 3 = 1000 L]
Hence, tank can hold 135000 L of water.

Ex 13.5 Class 9 Maths Question 3.
A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 m 3 of a liquid?
Solution.
Let h be the height of vessel.
Given, length (l) = 10 m and breadth (b) = 8 m
Volume of a cuboidal vessel = Liquid to be hold
∴ I x b x h = 380 [given]
⇒ 10 x 8 x h = 380
= h = = 4.75m
Hence, the cuboidal vessel must be made 4.75 m high.

Ex 13.5 Class 9 Maths Question 4.
Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of Rs. 30 per m 3
Solution.
Volume of a cuboidal pit = l x b x h = (8 x 6 x 3) = 144 m 3
[∵ l = 8 m, b = 6 m and h- 3 m, given]
∵ Cost of digging 1 m 3 cuboidal pit = Rs. 30
∴ Cost of digging 144 m 3 cuboidal pit = 30 x 144 = Rs. 4320

Ex 13.5 Class 9 Maths Question 5.
The capacity of a cuboidal tank is 50000 liters of water. Find the breadth of the tank, if its length and depth are 2.5 m and 10 m, respectively.
Solution.
Given, l = 2.5 m and h = 10 m
Let breadth of tank be b.

Ex 13.5 Class 9 Maths Question 6.
A village, having a population of 4000, requires 150 liters of water per head per day. It has a tank measuring 20 m x 15 m x 6 m. For how many days, will the water of this tank last?
Solution.
Given, length (l) = 20 m, breadth (b) = 15 m and height (h) = 6 m
∴ Capacity of the tank = Volume of the tank
= Ibh = (20 x 15 x 6) = 1800 m 3
∵ Water required for one person per day = 150 L
∴ Water required for 4000 persons per day

Ex 13.5 Class 9 Maths Question 7.
A godown measures 40 m x 25 m x 15 m. Find the maximum number of wooden crates each measuring 1.5 m x 1.25 m x 0.5 m that can be stored in the godown.
Solution.
Given, dimensions for godown are as length (l) = 40 m, breadth (b) = 25 m and height (b) = 15 m
Volume of the godown = l x b x h = 40m x 25m x 15m
Dimensions for each wooden crates are as

Ex 13.5 Class 9 Maths Question 8.
A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.
Solution.
Volume of a solid cube = 12 cm x 12 cm x 12 cm = 1728 cm 3
The solid cube is cut into eight cubes of equal volume.
Hence, the volume of the new cube = cm 3 =216cm 2
(side) 3 = 216 cm 3
side = 6 cm
Hence, side of the new cube = 6 cm
Surface area of solid cube = 6(side) 2 = 6(12) 2 cm 2
S1= 6 x 144 = 864 cm 2
Surface area of new cube = 6 (side) 2 = 6 (6) 2 cm 2
S2 = 216 cm 2
∴ Required ratio = S2 : S2
= 864 : 216 = 4:1

Ex 13.5 Class 9 Maths Question 9.
A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?
Solution.
Here, breadth of the river = 40 m
Depth of the river = 3 m
and length per hour of the river = 2 km = 2000 m
or length per minute of the river = m
∴ Water flowing per minute = x 40 x 3 = 4000 m 3

We hope the NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.5 help you. If you have any query regarding NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.5, drop a comment below and we will get back to you at the earliest.


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