A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 104 cm and the radius of each of the hemispherical ends is 7 cm, find the cost of polishing its surface at the rate of Rs 10 per dm^{2} .

#### Solution

We have a solid composed of cylinder with hemispherical ends.

Radius of the two curved surfaces(r) = 7 cm

Height of cylinder is *h*.

Total height of the body(h + 2r) = 104 cm

So, total surface area is given by,

Total surface area = Curved surface area of cylinder +2(Curves surface area of hemisphere)

=`2pirh+2(2pir^2)`

= 2πr(h+2r)

=2(3.14)(7)(104) cm^{2}

=4571.84 cm^{2}

Change the units of curved surface area as,

Total surface area = `4571.87/100 dm^2`

= 45.7184 dm^{2}

Cost of polishing the surface is Rs 10 per dm^{2}.

So total cost,

= Rs(45.7184)(10)

= Rs 457.18