A solid metal sphere is melted and smaller sperees of equal radii are formed. 10% of the volume of the sphere is lost in the process. The smaller spheres have a radius , that is `(1)/(9)` th the larger sphere . Iof 10 litres of paint were needed to paint the larger sphere. Find how many letres are needed to paint all the smaller spheres?

Explanation

Let radius of larger sphere =9r
radius of each smaller sphere =r
volume of larger sphere=`(4)/(3)pi(9r)^(3)`
From this larger sphere , let x small spheres are made but in this process 10% volume of larger sphere is lost.
`(4)/(3)pi(9r)^(3) -(10)/(100)xx(4)/(3)pi(9r)^(3)=xxx(4)/(3)pir^(3)`
`(9)/(10)xx(4)/(3)pir^(3)xx(9)^(3)=xxx(4)/(3)pir^(3) rarrx=(9^(4))/(10)`
Now paint needed in surface area `4pi(9r)^(2)rarr10 litre`
Paint needed in surface area `lrarr(10)/(4pir^(2)(9)^(2))xx(9^(4))/(10)`
Now paint needed in surface needed in surface area `4pi(9r^(2)) rarr` 10 litre
paint needed in surface area l `rarr (10)/(4pir^(2)(9^(2))` litre
paint needed in surface area `xxx4pir^(2)rarr(10)/(4pir^(2))(9^(2))xx(9^(4))/(10)xx4pir^(2)` litre=81 litre