Bihar Board Class 9th Maths Solutions Chapter 13 Surface Areas and Volumes Ex 13.5 Textbook Questions and Answers.

## BSEB Bihar Board Class 9th Maths Solutions 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:

Here l = 4 cm, b = 2.5 cm and h = 1.5 cm.

∴Volume of one matchbox = l x b x h cm³

= (4 x 2.5 x 1.5) cm³ = 15 cm³

∴ Volume of a packet containing 12 such boxes

= (12 x 15) cm³ = 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)

Solution:

Here l = 6m, 6 = 5m and h = 4.5 m

∴ Volume of the tank = Ibh m³

= (6 x 5 x 4.5) m³ = 135 m³

∴ The tank can hold = 135 x 1000 litres

= 135000 litres of water. [∵ 1 m³ = 1000 litres]

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 = 10 m, breadth = 8 m and volume = 380 m³

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 m³.

Solution:

Here, l = 8 m, b = 6 m and h = 3 m

Volume of the pit = lbh m³

= (8 x 6 x 3) m³ = 144 m³

Rate of digging is Rs 30-per m³

∴ Cost of digging the pit = Rs (144 x 30) = Rs 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 respectively 2.5 m and 10 m.

Solution:

Here, length = 2.5 m, depth = 10 m

and volume = 50000 litres

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:

Here, l = 20 m, 6 = 15 m and h = 6 m.

∴ Capacity of the tank = lbh m³

= (20 x 15 x 6) m³ = 1800 m³

Water requirement per person per day

= 150 litres

Water required for 4000 person per day

= (4000 x 150) l

= \(\left(\frac{4000 \times 150}{1000}\right)\) m³ = 600 m³

Number of days the water will last

Thus, the water will last for 30 days.

Question 7.

A godown measures 60 m x 25 m x 10 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:

Volume of the godown = (60 x 25 x 10) m³ = 15000 m³

Volume of 1 crates = (1.5 x 1.25 x 0.5) m³ = 0.9375 m³

Number 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.

Solution:

Let V_{1} = Volume of the cube of edge 12 cm = (12 x 12 x 12) cm³

V_{1} = Volume of the cube cut out of the first one

= \(\frac { 1 }{ 8 }\) x V_{1} = (\(\frac { 1 }{ 8 }\) x 12 x 12 x 12) cm³

= (6 x 6 x 6) cm³

∴ Side of the new cube = 6 cm

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:

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.

∴ The volume of water flowing into the sea in one hour

= Volume of the cuboid

= l x b x h m³

= (2000 x 40 x 3) m³

∴ The volume of water flowing into the sea in one minute

= \(\left(\frac{2000 \times 40 \times 3}{60}\right)\) m³

= 4000 m³.