Question

A bucket is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper circular ends as 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the bucket, at the rate of ₹ 40 per litre. (Use π = 3.14)

Answer 1

Height of a frustum of a cone, h = 16 cm R₁ = 8 cm and R₂ = 20 cm

Quantity of milk in a bucket

= `1/3 πh [R_1^2 + R_2^2 + R_1R_2]`

= `1/3 xx 3.14 xx 16(8)^2 + (20)^2 + 8 xx 20]`

= `(3.14 xx 16)/3 [64 + 400 + 160]`

= `(3.14 xx 16 xx 624)/3`

= 3.14 × 16 × 208 cm³

= `10449.92 xx 1/1000` litre

= 10.45 litre

Total cost of milk, which can completely fill the bucket

= ₹ 40 × 10.45 litre

= ₹ 418