# 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 = √((r1 - r2)2 + h2),
where r1 and r2 (r1 > r2) are radii of frustum and h is height of frustum

= = = 20 cm

The capacity of container = Volume of a 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 = Curved surface area of frustum + area of lower base

= 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 Rs.

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