Question

An open metal bucket is in the shape of a frustum of cone of height 21 cm with radii of its lower and upper ends are 10 cm and 20 cm respectively. Find the cost of milk which can completely fill the bucket at the rate of ₹ 40 per litre.

Answer 1

Let r₁ and r₂ be the radii of two circular ends and h be the height of frustum, then volume.

= `1/3 πh [r_1^2 + r_2^2 + r_1r_2]`

Given, r₁ = 10 cm, r₂ = 20 cm and h = 21 cm

∴ Volume = `1/3 xx 22/7 xx 21 xx [(10)^2 + (20)^2 + 10 xx 20]`

= 22[100 + 400 + 200]

= 22 × 700
= 15400 cm³

= `15400/1000` liters   ...(∵ 1000 cm³ = 1 liter)

= 15.4 liters

∴ Total cost of milk = 15.4 × ₹ 40

= ₹ 616

Hence, the cost of milk which can completely fill the bucket at the rate of ₹ 40 per liter is ₹ 616.