A container, opened from the top and 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 20cm, respectively. Find the cost of the milk which can completely fill the container, at the rate of Rs 20 per litre. Also find the cost of metal sheet used to make the container, if it costs Rs 8 per 100 cm2 (Take π = 3.14)
Radius (r1) of upper end of container = 20 cm
Radius (r2) of lower end of container = 8 cm
Height (h) of container = 16 cm
Slant height (l) of frustum
=
= 
= 
= 20 cm
Capacity of container = Volume of frustum
= 
h (r12 + r22 + r1r2)
= 
* 3.14 * 16 * [(20)2 + (8)2 + (20) (8)]
= 
* 3.14 * 16 (400 + 64 + 160)
= 
* 3.14 * 16 * 624
= 10449.92 cm3
= 10.45 litres
Cost of 1 litre milk = Rs 20
Cost of 10.45 litres milk = 10.45 × 20
= Rs 209
Area of metal sheet used to make the container
= π (r1 + r2) * l + πr22
= π (20 + 8) * 20 + π (8)2
= 560 π + 64 π
= 624 π cm2
Cost of 100 cm2 metal sheet = Rs 8
Cost of 624 π cm2 metal sheet = 
= 156.75