Question

A bucket is in the form of a frustum of a cone and it can hold 28.49 litres of water. If the radii of its circular ends are 28 cm and 21 cm, find the height of the bucket. [Use`pi22/7` ]

 

Answer 1

Let the height of the bucket be h cm.

Suppose r₁ and r₂ be the radii of the circular ends of the bucket.

Given, r₁ = 28 cm and r₂ = 21 cm

Capacity of bucket = 28.49 litres

∴Volume of the bucket = 28.49 × 1000 cm³ [1 litre = 1000 cm³]

`rArr1/3pih(r_1^2+r_2^2+r_1r_2)=28.49xx1000cm^3`

`rArr1/3xx22/7xxhxx[(28)^2+(21)^2+(28xx21)]cm^2=28490`

`rArr22/21xxhxx1813=28490 cm`

`rArrh=(28940x21)/(22xx1813)cm`

`h=15cm`

Thus, the height of the bucket is 15 cm.