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What length of tarpaulin 3 m wide will be required to make a conical tent of length 8 m and base radius 6 m? Assume that the extra length of material required for stitching margins and wastage in cutting will be approximately 20 cm.

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62.05m

64m

63.05m

65m

answer is C.

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Detailed Solution

Given,
length of conical tent (h) = 8 m.
radius of the conical tent (r) = 6 m.
Slant height (l)

= r 2 + h 2

⇒ 62 + 82

⇒ 100

⇒ 10

m
Curved surface area of a cone

= π r l

⇒ 227 × 6 × 10

⇒ 188.57 m 2

We know, Area of the tarpaulin = Curved surface area of the tent
As the tarpaulin is in the shape of a rectangle.
So, Area of the rectangle = length

width
Given, width of the tarpaulin = 3 m.
length

×

3 = 188.57

⇒

62.85 m
Given, stitching margin and wastage in cutting = 20 cm

⇒

0.2 m [100cm=1m]
Total length with stitching margin

= 62.85 + 0.2

⇒

63.05 m
Therefore, the correct option is 3.

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