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Question
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 m2, 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 m2 area.
`"Rs. 2200 is the cost of painting "=(1/20xx2200)m^2" area"`
= 110 m2 area
Therefore, the inner surface area of the vessel is 110 m2.
(ii) Let the radius of the base of the vessel be r.
Height (h) of vessel = 10 m
Surface area = 2πrh = 110 m2
`rArr(2xx22/7xxr xx10)m = 110m^2`
`rArr r=(7/4)m = 1.75m`
(iii) Volume of vessel = πr2h
`=[22/7xx(1.75)^2xx10]m^3`
= 96.25 m3
Therefore, the capacity of the vessel is 96.25 m3 or 96250 litres.
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