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A bucket is in the form of a truncated cone. The diameters of the base and top of the bucket are 6 cm and 12 cm respectively. If the height of the bucket is 7 cm, what is the capacity of the bucket?

A bucket is in the form of a truncated cone. The diameters of the base and top of the bucket are 6 cm and 12 cm respectively. If the height of the bucket is 7 cm, what is the capacity of the bucket? Correct Answer 462 cm<sup>3</sup>

We can say that the bucket is in the form of frustum:

r = 3 cm and R = 6 cm, h = 7 cm

Now,

Volume of the frustum = π/3(r2 + R2 + rR)h

⇒ π/3(32 + 62 + 18) × 7

⇒ 22/21 × (32 + 62 + 18) × 7

⇒ 22 × (9 + 36 + 18)

⇒ 22/3 × 63

⇒ 462 cm3

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