Question

Question 12
A milk container of height 16 cm is made of metal sheet in the form of a frustum of a cone with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk at the rate of Rs. 22 per litre which the container can hold.

Answer 1

Given that, height of milk container (h) = 16 cm.
Radius of lower end of milk container (r) = 8 cm
And radius of upper end of milk container (R) = 20 cm

$\therefore$ Volume of the milk container made of metal sheet in the form of a frustum of a cone
$=\frac{\pi h}{3}(R^2+r^2+Rr)=\frac{22}{7}\times \frac{16}{3}\left[\right(20{)}^2+(8{)}^2+20\times 8]=\frac{22\times 16}{21}(400+64+160)=\frac{22\times 16\times 624}{21}=\frac{219648}{21}[\because 1L=100c{m}^3]=10459.42c{m}^3=10.45942L$
So, volume of the milk container is 10459 . $42c{m}^3$
$\because$ Cost 1 L milk = Rs 22
$\because$ Cost of 10.45942 L milk =$22\times 10.45942$ = Rs 230.12
Hence, the required cost of milk is Rs 230.12