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

NCERT Solutions Class 9 Maths
Chapter – 13 (Surface Areas and Volumes)

The NCERT Solutions in English Language for Class 9 Mathematics Chapter – 13 Surface Areas and Volumes Exercise 13.5 has been provided here to help the students in solving the questions from this exercise.

Chapter 13: Surface Areas and Volumes

Exercise – 13.5

1. A matchbox measures 4 cm×2.5 cm×1.5 cm. What will be the volume of a packet containing 12 such boxes?

Answer –
Length of the matchbox, l = 4 cm,
Breadth of the matchbox, b = 2.5 cm,
Height of the matchbox, h = 1.5 cm
NCERT Class 9 Solutions Maths
The volume of each matchbox = l × b × h
= 4 cm × 2.5 cm × 1.5 cm
= 15 cm³Volume of 12 matchboxes = 12 × 15cm³ = 180cm³Thus, the volume of the packet containing 12 such matchboxes is 180 cm³.

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)

Answer –
Length of the cuboidal tank, l = 6 m,
Breadth of the cuboidal tank, b = 5 m,
Height of the cuboidal tank, h = 4.5 m
Volume of the cuboidal tank = l × b × h
V = 6m × 5m × 4.5m
V = 135 m³V = 135 × 1000L
V = 135000L (1m³ = 1000L)
Thus, the cuboidal water tank can hold 135000 litres of water.

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?

Answer –
Let the height of the cuboidal vessel = h
Length of the cuboidal vessel, l = 10 m
The breadth of the cuboidal vessel, b = 8 m
The capacity of the cuboidal vessel (V) = 380 m³Volume of the liquid in the cuboidal vessel = l × b × h
l × b × h = 380m³10 m × 8 m × h = 380m³h = 380 / (10 × 8)
h = 4.75 m
Thus, the cuboidal vessel must be made 4.75 m high.

4. Find the cost of digging a cuboidal pit of 8 m long, 6 m broad and 3 m deep at the rate of Rs. 30 per m³.

Answer –
Length of the cuboidal pit, l = 8 m
Breadth of the cuboidal pit, b = 6 m
Height of the cuboidal pit, h = 3 m
Volume of the cuboidal pit = l × b × h
= 8m × 6m × 3m
= 144 m³Thus, the cost of digging the pit at ₹ 30 per m³ = ₹ 30 × 144 = ₹ 4320

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.

Answer –
Let the breadth of the cuboidal tank = b
Length of the cuboidal tank, l = 2.5 m
Height of the cuboidal tank, h = 10 m
The capacity of the tank = 50000L
= 50000/1000 m³ (∵ 1m³ = 1000L)
= 50 m³Volume of the cuboidal tank = l × b × h
l × b × h = 50 m³b = 50 m³/l × h
b = 50 m³/(2.5m × 10m)
= 2 m
Therefore, the breadth of the tank is 2 m.

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 in this tank last?

Answer –
Length of the tank, l = 20 m
Breadth of the tank, b = 15 m
Height of the tank, h = 6 m
The volume of the water in the tank = l × b × h
= 20m × 15m × 6m
= 1800 m³Total population of the village = 4000
Requirement of water per head per day is 150 litres.
Requirement of water per day for 4000 population = 4000 × 150L
= 600000L
= 600000/1000 m³ (∵ 1000L = 1 m³)
= 600 m³
Number of days for which the water of the tank will last = 1800m³/600m³ = 3 days

7. A godown measures 40 m×25 m×15 m. Find the maximum number of wooden crates, each measuring 1.5m × 1.25 m × 0.5 m, that can be stored in the godown.

Answer –
Length of the godown, L = 40 m
Breadth, B = 25 m
Height, H = 15 m
Capacity of the godown = L × B × H
= 40m × 25m × 15m
= 15000 m³Length of the crate, l = 1.5 m
Breadth of the crate, b =1.25 m
Height of the crate, h = 0.5 m
Volume of each crate = l × b × h
= 1.5m × 1.25m × 0.5m
= 0.9375 m³Number of crates = 15000m³/0.9375m³ = 16000
The maximum number of wooden crates that can be stored in the godown is 16000.

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.

Answer –
Side of the cube = 12 cm
The volume of the solid cube = a³= (12 cm)³= 1728 cm³The cube is cut into 8 equal cubes of the same volume.
Volume of each small cube = (1/8) × 1728 cm³ = 216 cm³Let ‘x’ be the side of each small cube.
Volume of each small cube = x³ = 216 cm³x³ = (6 cm)³ [Since 6³ = 216]
x = 6 cm
Surface area of the solid cube = 6a²Surface area of the small cube = 6x²Ratio between their surface areas = 6a²/6x²= a²/x²= (a/x)²= (12/6)²= 4/1
The side of the new cube is 6 cm and the ratio between the surface areas is 4 : 1.

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?

Answer –
Width of the river, b = 40 m
Depth of the river, h = 3 m
Flowing rate of water = 2 km / h
= 2000 m / 60 min
= 100/3 m/min
Length of the water flowing in 1 minute, l = 100/3 m
The volume of the water that falls into the sea in 1 minute = l × b × h
= 100/3 m × 40 m × 3 m
= 4000 m³Thus, 4000 m³ of water will fall into the sea in a minute

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