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

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

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

NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.5 are the part of NCERT Solutions for Class 9 Maths. Here you can find the NCERT Solutions for Chapter 13 Surface Areas and Volumes Ex 13.5.

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

Ex 13.5 Class 9 Maths Question 1.
A matchbox measures 4 cm × 2.5 cm × 1.5 cm. What will be the volume of a packet containing 12 such boxes?

Solution:
Since, a matchbox is in the shape of a cuboid.
Here, length (l) = 4 cm, breadth (b) = 2.5 cm and height (h) = 1.5 cm
Volume of a matchbox = l × b × h
= 4 × 2.5 × 1.5 cm3
= 15 cm3
Volume of 12 such boxes = 12 × 15 cm3 = 180 cm3

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 litres of water can it hold? (1 m3 = 1000 L)

Solution:
Here, Length (l) = 6 m, breadth (h) = 5 m and depth (h) = 4.5 m
Capacity = l × b × h = 6 × 5 × 4.5 m3
= 30 × 4.5 = 135 m3
1 m3 = 1000 litres

135 m3 = 135000 litres
The required amount of water in the tank = 135000 litres.

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 cubic metres of a liquid?

Solution:
Here, Length (l) = 10 m, breadth (b) = 8 m and Volume (V) = 380 m3
Let height of the cuboidal vessel be ‘h’.
Volume of the cuboidal vessel = l × b × h
10 × 8 × h m3 = 80h m3
80h = 380
h = 380/80 = 4.75 m
Thus, the required height of the vessel = 4.75 m

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 ₹30 per m³.

Solution:
Here, Length (l) = 8 m
Depth (h) = 3 m
Volume of the cuboidal pit = l × b × h
= 8 × 6 × 3 m3 = 144 m3
Hence, the cost of digging a pit = ₹  (144 × 30)
= ₹ 4320

Ex 13.5 Class 9 Maths 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:
Length of the tank (l) = 2.5 m
Depth of the tank (h) = 10 m
Let breadth of the tank be b m.
Volume (capacity) of the tank = l × b × h
= 2.5 × b × 10 m3
= 25b m3

But the capacity of the tank = 50000 litres
= 50 m3 [
1000 litres = 1 m3]
25b = 50 b = 50/25 = 2
Thus, the breadth of the tank = 2 m

Ex 13.5 Class 9 Maths 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 × 15 m × 6 m. For how many days will the water of this tank last?

Solution:
Length of the tank (l) = 20 m
Breadth of the tank (b) = 15 m
Height of the tank (h) = 6 m
Volume of the tank = l × b × h
= 20 × 15 × 6 m3 = 1800 m3
Since, 1 m3 = 1000 litres
Capacity of the tank = 1800 × 1000 litres = 1800000 litres
Since, 150 litres of water is required per head per day.
Amount of water required by 4000 people per day = 150 × 4000 litres
Let the required number of days be x.
4000 × 150 × x = 1800000

600000 × x = 1800000
x = 1800000/600000 = 3
Thus, the required number of days is 3.

Ex 13.5 Class 9 Maths Question 7.
A go down measures 40 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 go down.

Solution:
Volume of the go down = 40 × 25 × 10 m3
Volume of a wooden crate = 1.5 × 1.25 × 0.5 m3

Maximum number of wooden crates = 10667.

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:
Side of the given cube = 12 cm
Volume of the given cube = (side)3 = (12)3 cm3 = 1728 cm3
Let the side of the new cube be n.

Volume of new cube = n3
Volume of 8 new cubes = 8n3
According to question,
8n3 = 1728
n3 = 1728/8 = 216
n3 = 63
n = 6
Thus, the required side of the new cube is 6 cm.
Now, surface area of the given cube = 6 × (side)2 = 6 × 122 cm2 = 6 × 12 × 12 cm2
Surface area of new cube = 6 × 62 cm2
= 6 × 6 × 6 cm2
Now,

Thus, the required ratio = 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:
The water flowing in a river can be considered in the form of a cuboid.

Length (l) = 2 km = 2000 m
Depth (h) = 3 m
Volume of water (volume of the cuboid so formed) = l × b × h
= 2000 × 40 × 3 m3
Now, volume of water flowing in 1 hr (60 minutes) = 2000 × 40 × 3 m3
Volume of water that will fall in 1 minute
= [2000 × 40 × 3] ÷ 60 m3
= 4000 m3

You can also like these:

NCERT Solutions for Maths Class 10

NCERT Solutions for Maths Class 12