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A tent is in the shape of a right circular cylinder up to a height of $3 m$ and conical above it. The total height of the tent is $13.5 m$ above the ground. What is the cost of painting the inner side of the tent at the rate of Rs.2 per $m 2$ , if the radius of the base is $14 m$ ?

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Rs.2068

Rs.2008

Rs.2000

Rs.2080

answer is A.

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Detailed Solution

Given that a right circular cylinder up to a height of

3 m

, total height of the tent is

13.5 m

, the radius of the base is

14 m

and the rate of painting is Rs.2 per

m 2

.
We have the formulae,
CSA of cone =

π r h

CSA of cylinder =

2 π r h

Slant height

l 2 = r 2 + h 2

CSA of cylinder will be,

2 × 227 × 14 × 3 = 264 m 2

Height of the tent = total height – height of the cylinder

= 13.5 − 3 = 1 0. 5

Then,

l 2 = 142 + 10.5 2 l 2 = 196 + 110.25 l 2 = 306.25 l = 306.25 l = 17.5 m

CSA of cone will be,

= 227 × 14 × 17.5 = 770 m 2

Required surface area = CSA of cylinder +CSA of cone

= 264 + 770 = 1034 m 2

The cost of cloth is Rs.2 per

m 2

then the cost of 1034

of cloth will be,

= 1034 × 2 = R s .2068

Thus, the cost is Rs.2068.
Therefore the correct option is 1.

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