find its surface area

Question

the total cost of making a spherical metal ball at the rate of rs.7 m3 rs.33957.find its surface area

Answer 1

Rs33957 will pay for 33957/7=4851 cu metres of metal. The volume of a ball is 4πr^3/3 where r is its radius. The surface area of the ball is 4πr^2. So if 4πr^3/3=4851, r^3=14553/(4π)=1158.09, from which r=10.5m approx. The ratio of volume to surface area is 4πr^3/(12πr^2)=r/3. So V/S=r/3 and S=3V/r where V=volume and S=surface area. So S=4851*3/10.5=1385.51 sq m.