Sum

The radii of two circular ends of a frustum shape bucket are 14 cm and 7 cm. The height of the bucket is 30 cm. How many liters of water it can hold?

(1 litre = 1000 cm

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#### Solution

Radius of one circular end, r_{1} = 14 cm

Radius of other circular end, r_{2 }= 7 cm

Height of the bucket, h = 30 cm

∴ Volume of water in the bucket = Volume of frustum of cone

\[= \frac{1}{3}\pi h\left( r_1^2 + r_1 r_2 + r_2^2 \right)\]

\[ = \frac{1}{3} \times \frac{22}{7} \times 30 \times \left( {14}^2 + 14 \times 7 + 7^2 \right)\]

\[ = \frac{1}{3} \times \frac{22}{7} \times 30 \times 343\]

\[ = 10780 {cm}^3\]

\[= \frac{10780}{1000}\]

\[ = 10 . 780 L\]

Thus, the bucket can hold 10.780 litres of water.

Concept: Frustum of a Cone

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