PSEB Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.5
PSEB Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.5
PSEB 9th Class Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.5
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 ?
Answer:
For the cuboidal matchbox, length l = 4 cm; breadth b = 2.5 cm and height h = 1.5 cm.
Volume of a cuboidal matchbox
= l × b × h
= 4 × 2.5 × 1.5 cm3
= 15 cm3
Then, volume of 12 matchboxes = 12 × 15 cm3 = 180 cm3
Thus, the volume of a packet containing 12 matchboxes is 180 cm3.
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)
Answer:
For the cuboidal water tank, length l = 6m; breadth b = 5 m and height h = 4.5 m.
Capacity of the cuboidal tank = l × b × h
= 6 × 5 × 4.5 m3
= 135 m3
1 m3 = 1000 litres
∴ 135 m3 = 135000 litres
Thus, the given cuboidal water tank can hold 1,35,000 litres of water.
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?
Answer:
For the cuboidal vessel, length l = 10 m;
breadth b = 8 m and capacity = 380 m3.
Capacity of a cuboidal vessel = l × b × h
∴ 380 m3 = 10 m × 8 m × h m
∴ h = 380/10×8 m
∴ h = 4.75 m
The height of the cuboidal vessel must be made 4.75 m.
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.
Answer:
For the cuboidal pit, length l = 8m; breadth b = 6 m and height (depth) h = 3 m.
Volume of the earth to be dugout to make the cuboidal pit = Volume of a cuboid
= l × b × h
= 8 × 6 × 3 m3
= 144 m3
Cost of digging out 1 m3 of earth = ₹ 30
∴ Cost of digging out 144 m3 of earth
= ₹ (30 × 144)
= ₹ 4320
Thus, the cost of digging the cuboidal pit is ₹ 4320.
Question 5.
The capacity of a cuboidal tank is 50,000 litres of water. Find the breadth of the tank, if its length and depth are respectively 2.5 m and 10 m.
Answer:
For the cuboidal tank, length l = 2.5 m;
height (depth) h = 10 m and
capacity = 50,000 litres.
1000 litres = 1 m3
∴ 50,000 litres = 50,000/1000 m3 = 50 m3
Capacity of cuboidal tank = l × b × h
∴ 50 m3 = 2.5 m × b m × 10 m
∴ b = 50/2.5×10 m
∴ b = 2 m
Thus, the 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 × 15 m × 6 m. For how many days will the water of this tank last?
Answer:
Total requirement of water per day
= No. of people × daily requirement per person
= 4000 × 150 litres
= 6,00,000 litres
= 6,00,000/1000 m3
= 600 m3
For the cuboidal tank, length l = 20 m;
breadth b = 15 m and height h = 6 m
Capacity of the cuboidal tank = l × b × h
= 20 × 15 × 6 m3
= 1800 m3
600 m3 of water can last for 1 day in the village.
∴ 1800 m3 of water can last for 1800/600 = 3 days in the village.
Question 7.
A godown measures 40 m × 25 m × 15 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.
Answer:
For the cuboidal godown, length l = 40 m;
breadth b = 25 m and height h = 15 m.
Capacity of cuboidal godown = l × b × h
= 40 × 25 × 15 m3
For the wooden cuboidal crate, length l = 1.5 m; breadth b = 1.25 m and height h = 0,5 m.
Volume of 1 cuboidal crate
= l × b × h
= 1.5 × 1.25 × 0.5 m3
∴The no. of crates that can be stored in the godown =
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.
Answer:
For the original cube, edge a =12 cm.
Volume of original cube = a3 = 123 cm3
= 1728 cm3
8 cubes of equal volume are made from the original cube.
Thus, the required ratio of the total surface area of the original cube and the total surface area of a new cube is 4:1.
Note: If the ratio of TSA of the original ‘ cube and TSA of all the new cubes is required, then it will be 1 : 2.
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?
Answer:
2 km = 2000 m and 1 hour = 60 minutes
Rate of flow of water in the river
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