Question

A storage tank consists of a circular cylinder with a hemisphere stuck on either end. If the external diameter of the cylinder be $$1.4\ m$$. and its length be $$8\ m$$. Find the cost of painting it on the outside at rate of $$Rs\ 20\ per\ m^{2}$$.

Answer 1

Total surface area of a tank= $$2\times$$ curved surface area of hemisphere + curved surface area of cylinder
Radius of hemisphere $$=\dfrac{d}{2}=\dfrac{1.4}{2}=0.7\ m$$
Curved surface area of hemisphere
$$=2\pi r^{2}=2\times \dfrac{22}{7}\times 0.7\times 0.7=3.08\ m^{2}$$
$$2\times$$ curved surface area of hemisphere
$$=2\times 3.08\ m^{2}=6.16\ m^{2}$$
Radius of cylinder, $$r=\dfrac{d}{2}=\dfrac{1.4}{2}=0.7\ m$$
Height of cylinder, $$h=8\ m$$
Curved surface area of the cylinder
$$=2\pi rh =2\times \dfrac{22}{7}\times 0.7\times 8=35.2\ m^{2}$$
Total surface area of the storage tank
$$=35.2+6.16=41.36\ m^{2}$$
Cost of painting its surface area at
$$Rs\ 20\ per\ m^{2}=41.36\times 20=Rs. 827.2$$