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 20 cm respectively. Find
(i) the cost of metal sheet used to make the container if it costs Rs 10 per 100 cm2
(ii) the cost of milk at the rate of Rs 35 per litre which can fill it completely.
(i)
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, l=√(r1−r2)2+h2=√(20−8)2+162=√122+162=√144+256=√400=20 cm
Capacity of container = Volume of frustum
=13πh(r21+r22+r1r2)=13×3.14×16×(202+82+20×8)=13×3.14×16×(400+64+160)=13×3.14×16×624=10449.92 cm3=10.45 litres
(ii) Cost of 1 litre milk = Rs 35
Cost of 10.45 litre milk = 10.45 × 35
= Rs 365.75
(i) Area of metal sheet used to make the container
=π(r1+r2)l+πr22=π(20+8)l+π82=560π+64π=624π cm2
Cost of 100 cm2 metal sheet = Rs 10
cost of 624π cm2 metal sheet =624×3.14×10100=195.94
Therefore, the cost of the milk which can completely fill the container is
Rs 365.75 and the cost of metal sheet used to make the container is Rs 195.94.