Question

A container made up of a metal sheet is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of the milk which can completely fill the container at the rate of ₹ 15 per litre. (Take $\pi$= 3·14)

• A. 92.45
• B. 95.63
• C. 97.97
• D. 100

Answer 1

The correct option is D

100

R = 20 cm, r = 8cm, h = 16 cm

Volume of container $=\frac{1}{3}\pi h\{R^2+r^2+Rr\}$

= $\frac{1}{3}$ $\times$ (3.14) $\times$ 16 { 400 + 64 + 160 } $c{m}^3$

= 3.14 $\times$ 16 $\times \frac{1}{3}$ {624} $c{m}^3$

= 3.14 $\times$ 16 $\times$ 208 $c{m}^3$

= 10449.93 $c{m}^3$

Therefore, the quantity of milk in the container = $\frac{10449.92}{1000}$ liters = 10.45 liters

Cost of milk at the rate of ₹15 per liters = ₹ {10.45 × 15 } = ₹ 156.75