Surface Area and Volumes – Exercise 13.5 – Class IX

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:

Volume of 1 match box = lbh [here, l = 4cm , b = 2.5cm, h = 1.5cm]

= 4 x 2.5 x 1.5

= 15 cm³

Volume of 12 such match boxes = 15 x 12 = 180 cm³

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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:

Volume of  water tank = lbh [here, l = 6m , b = 5m, h = 4.5m]

= 6 x 5 x 4.5

= 135 m³

Capacity of water tank for 1m³ = 1000litres

Then, capacity of water tank for 135m³ = 135 x 1000 = 135000 litres

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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 cuboidal vessel  = lbh [here, l = 10m , b = 8m, volume = 380m³]

380 = 10 x 8 x h

h = ³⁸⁰/_10×8

h = 4.75 m

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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:

Volume of cuboidal pit = lbh

= 8 x 6 x 3

= 144 m³

The cost of digging cuboidal pit for 1m³ = Rs. 30

The cost of digging cuboidal pit for 144m³ = 144 x 30 = Rs. 4320

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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:

Given length of tank = 2.5m and height 10 m

capacity of water tank = 50000 litres = ⁵⁰⁰⁰⁰/₁₀₀₀ m³ = 50m³

Capacity of water tank = volume of water tank = lbh

50 = 2.5 x b x 10

b = ⁵⁰/_2.5×10 = 2 m

i.e., breadth of the tank = 2m

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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:

Given, a village, having a population of 4000, requires 150 litres of water per head per day.

Water required for 1 person for one day = 150 litres

Therefore, water required for 4000 peoples for one day  = 150 x 4000 = 6,00,000 litres

Volume of the water tank = lbh

l = 20m , b = 15 m and h = 6m

Volume of watertank = 20 x 15 x 6

= 1800m³

Water holding capacity of the tank = 1800 x 1000 = 18,00,000 litres.

Thus, the number of days will the water of this tank last = ^{water holding capacity of the tank}/_{water  required for 4000 peoples for one day}

= ^18,00,000/_6,00,000 = 3

Hence, one tank of water will last for 3 days.

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7. A godown 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 godown.

Solution:

Volume of godown = lbh [here l = 40m, b = 25m , h = 10m]

= 40 x 25 x 10

= 10000 m³

Volume of the wooden crates = lbh [l = 1.5m , b = 1 .25m , h = 0.5 m]

= 1.5 x 1.25 x 0.5

= 0.9375 m³

No. of wooden crates stored in godown = ^{Volume of godown}/ _{Volume of the wooden crates}

= ¹⁰⁰⁰⁰/_0.9375

= 10666. 67

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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 cube = a³

= 12³

= 1728 cm³

Given, solid cube of side 12 cm is cut into eight cubes of equal volume. i.e., = ¹⁷²⁸/₈ = 216 cm³

Therefore, volume of the each new cube = 216 cm³

We know, volume of each new cube = (s)³

216 = s³

s = 6 cm

The ratio between volume of a soild cube and volume of new cube = 12 : 6 = 2 : 1

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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:

h = 3 m ; b = 40 m ;

Water flow for 1 hour, l = 2 km = 2000m

Volume of water flowing through the river in 1 hour = lbh

= 2000 x 3 x 40

= 240000 m³

Volume of water flowing in 1 minute = ²⁴⁰⁰⁰⁰/₆₀ = 4000 m³

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