It costs Rs 2200 to paint the inner curved surface of a cylindrical vessel 10m deep. If the cost of painting is at the rate of Rs 20 per m2, find
(i) inner curved surface area of the vessel
(ii) radius of the base
(iii) capacity of the vessel
(Assume π = 22/7)
(i) Rs 20 is the cost of painting 1 m2 area.
Rs 1 is the cost to paint 1/20 m2 area
So, Rs 2200 is the cost of painting = (1/20 × 2200) m2
= 110 m2 area
The inner surface area of the vessel is 110m2.
(ii) Radius of the base of the vessel, let us say r.
Height (h) = 10 m and
Surface area formula = 2πrh
Using result of (i)
2πrh = 110 m2
2 × 22/7 × r × 10 = 110
r = 1.75
Radius is 1.75 m.
(iii) Volume of vessel formula = πr2h
Here r = 1.75 and h = 10
Volume = (22/7) × (1.75)2 × 10 = 96.25
Volume of vessel is 96.25 m3
Therefore, the capacity of the vessel is 96.25 m3 or 96250 litres.