Question

A bucket is frustum-shaped. Its height is 28 cm. Radii of circular faces are 12 cm and 15 cm. Find the capacity of the bucket in litres. `(π = 22/7)`

Answer 1

Given:

Frustum-shaped bucket with height h = 28 cm,

Radii: r1 = 15 cm and r2 = 12 cm,

Use `π = 22/7`

Using the formula Volume of a frustum:

V = `(1/3) xx π xx h xx (r1^2 + r2^2 + r1 xx r2)`

Substituting values:

V = `(1/3) xx (22/7) xx 28 xx (15^2 + 12^2 + 15 xx 12) `

= `(1/3) xx (22/7) xx 28 xx (225 + 144 + 180)`

= `(1/3) xx (22/7) xx 28 xx 549`

= `1/3` × 22 × 4 × 549

= `1/3` × 88 × 549

= `(88 xx 549)/3`

= `48312/3`

∴ V = 16104 cm³

Converting to litres (1 litre = 1000 cm³): 

V = `16104/1000`

∴ V = 16.104 litres

Hence, Capacity = 16104 cm³ = 16.104 litres (≈ 16.10 L).