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Due to heavy floods in the state, thousands were rendered homeless. 50 schools collectively offered to the state government to provide a place and the canvas for 1500 tents to be fixed by the government and decided to share their whole expenditure equally. The lower part of each tent is cylindrical of base radius $2.8 m$ and height $3.5 m,$ with conical upper part of same base radius but of height $2.1 m$ . If the canvas used to make the tents cost Rs.120 per $m 2$ , then what is the amount shared by each school to set up the tents taking $π = 227$ ?

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Rs.3, 32,600

Rs.3, 33,640

Rs.3, 32,640

Rs.3, 22,220

answer is C.

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Detailed Solution

Given that the number of schools are 50, number of tents are 1500, radius of base is 2.8m height is 3.5m, height of the conical upper part is 2.1m and the cost will be Rs.120 per

m 2

.
Slant height is

l 2 = h 2 + r 2

For cone,

l 2 = h 2 + r 2 l = h 2 + r 2 = (2.1) 2 + (2.8) 2 = 3.5 m

CSA of cone =

π r l

CSA of cylinder =

2 π r h

Area of 1 tent = CSA of cone + CSA of cylinder

= π r l + 2 π r h = π r (l + 2 h) = 227 × 2.8 [2 (3.5) + 3.5] = 92.4 m 2

Canvas required for 1500 tents =

1500 × Area of 1 tent

= 1500 × 92.4 = 138, 600 m 2

Cost of making 1500 tents,

= 120 × 138.600 = R s .1, 66, 32, 000

The amount shared by each school is,

= Total amount Number of schools = 1663200050 = R s .3, 32, 640

Thus the amount shared by each school is Rs.3, 32,640.
Therefore the correct option is 3.

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