Question

A bucket of height 24 cm is in the form of frustum of a cone whose circular ends are of diameter 28 cm and 42 cm. Find the cost of milk at the rate of Rs 30 per litre, which the bucket can hold.

Answer 1

We have,

Height of the frustum, h = 24 cm,

Radius of the open end, R = $\frac{42}{2}$ = 21 cm and

Radius of the close end, r = $\frac{28}{2}$ = 14 cm

Now,

Volume of the bucket = $\frac{1}{3}$$\pi h(R^2+r^2+Rr)$
= $\frac{1}{3}$×$\frac{22}{7}$ ×24×$({21}^2+{14}^2+21\times 14)$

= $\frac{176}{7}$×(441+196+294)

= $\frac{176}{7}$ × 931

= 23408 $c{m}^3$

= 23.408 L (As, 1000 $c{m}^3$ = 1 L)

Therefore, The cost of the milk = 30 × 23.408 = 702.24

So, the cost of the milk which the bucket can hold is Rs. 702.24.