This is one of the important question from the cbse board exam point of view because in 2013 and 2017 cbse board exam this question was asked. Question number 5 from RS Aggarwal book page number 823, exercise 17C, chapter volume and surface area of solid.

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# A container made of a metal sheet open at the top is of the form of frustum of cone, whose height is 16 cm and the radii of its lower and upper circular edges are 8 cm and 20cm respectively. Find i] the cost of metal sheet used to make the container if it costs 10 per 100 cm² , ii] the cost of milk at the rate of 35 per litre which can fill it completely.

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Given data

Radius of lower end = r = 8 cm

Radius of upper end = R = 20 cm

Height of container frustum = h = 16 cm

Cost of 100 cm

^{2}metal sheet = Rs 10So, Cost of 1 cm

^{2}metal sheet = 10/100 = Rs 0.1Let l be the slant height.

l

^{2}= (R-r)^{2}+ h^{2}= (20-8)

^{2}+ 16^{2}= 256 + 144

= 400

or l= 20cm

Surface area of frustum of the cone = πr

^{2}+ π(R + r)l cm^{2}= π[ (20 + 8 )20 + 8

^{2}]= π[560 + 64]

= 624 X ( 22/7 )

= 1961.14 cm

^{2}(i) Find cost of metal sheet used to make the container if it costs Rs. 10 per 100 cm

^{2}Cost of metal sheet per 100 cm

^{2}= Rs. 10Cost of metal for Rs. 1961.14 cm

^{2}= (1961.14 x10)/100 = Rs. 196.114(ii) Find the volume of frustum:

Volume of frustum = 1/3 πh(r

^{2}+ R^{2}+ rR)= 1/3 x 22/7 x 16(8

^{2}+ 20^{2}+ 8×20)= 1/3 x 22/7 x 16(64 + 400 + 160)

= 10345.4208 cm

^{3}= 10.345 liters

Using

1000cm

^{3}= 1 litre1 cm

^{3 }= 1/1000 litreCost of 1 liter milk = Rs. 35

Cost of 10.345 liter milk = Rs. 35 x 10.345

= Rs. 363