It costs Rs 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of Rs 20 per m^{2}, find

(i) Inner curved surface area of the vessel

(ii) Radius of the base

(iii) Capacity of the vessel

`["Assume "pi=22/7]`

#### Solution

(i) Rs 20 is the cost of painting 1 m^{2} area.

`"Rs. 2200 is the cost of painting "=(1/20xx2200)m^2" area"`

= 110 m^{2} area

Therefore, the inner surface area of the vessel is 110 m^{2}.

(ii) Let the radius of the base of the vessel be* r*.

Height (*h*) of vessel = 10 m

Surface area = 2π*rh* = 110 m^{2}

`rArr(2xx22/7xxr xx10)m = 110m^2`

`rArr r=(7/4)m = 1.75m`

(iii) Volume of vessel = π*r*^{2}*h*

`=[22/7xx(1.75)^2xx10]m^3`

= 96.25 m^{3}

Therefore, the capacity of the vessel is 96.25 m^{3} or 96250 litres.