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A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are $2.1 m$ and $4 m$ respectively and the slant height of the top is $2.8 m$ , then what is the area of the canvas used for making the tent and also the cost of the canvas of the tent at the rate of Rs.500 per $m 2$ .

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Rs.

32000

Rs.

24000

Rs.

22000

Rs.

20000

answer is C.

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Detailed Solution

Given that the height and diameter of the cylindrical part are 2.1m and 4m, the slant height of the top is

2.8 m

and the rate is Rs.500 per

m 2

.
We have the following formulae,
Curved area of conical part =

π r l

Curved area of cylindrical part =

2 π r h

Then for cone,
r = 2m
l = 2.8m
Cylinder,
r = 2m
h = 2.1m
Area canvas used will be,
Curved Area of conical part + Curved Area of cylindrical part

= π × 2 × 2.8 + 2 π × 2 × 2.1 = 2 π [2.8 + 4.2] = 2 × 227 × 7 = 44 m 2

Cost of

1 m 2

canvas is Rs.500
Cost of

44 m 2

canvas is,

44 × 500 = R s .22000

Thus, the cost is Rs.

22000

.
Therefore the correct option is 3.

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