Question

A bucket is in the form of frustum of cone. It holds 28,490 litres of water. The radii of the top and the bottom are 28 cm and 21 cm respectively. Find the height of the bucket.`(pi = 22/7)`

Answer 1

Volume of bucket = 28.490 litres

Volume of frustum (V) = 28490 cm³

r₁ = 28 cm, r₂ = 21 cm

Volume of bucket = `1/3 pi h(r_1^2 + r_2^2 + r_1 xx r_2)`

`28490 = 1/3 xx 22/7 xx h (28^2 + 21^2 + 28^2 xx 21)`

`therefore 28490 = 1/3 xx 22/7 xx h(784 + 441 + 588)`

`therefore 28490 = 1/3 xx 22/7 xx h xx 1813`

`(28490 xx 3 xx 7)/(22 xx 1813) = h`

∴ h = 15

∴ Height of the bucket is 15 cm.