Mathematics
If you are given a rectangular canvas of 1.5 m in width, what length of this canvas would you require to make a conical tent that is 48 m in diameter and 7 m in height? Note that 10% of the canvas is used (wasted) in folds and stitchings.
Also, find the cost of the canvas at the rate of ₹24 per meter.
Mensuration
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Answer
Given,
Diameter of tent = 48 m
Radius (r) = = 24 m
Height (h) = 7 m
Slant height = l
We know that,
⇒ l2 = h2 + r2
⇒ l2 = 72 + 242
⇒ l2 = 49 + 576
⇒ l2 = 625
⇒ l =
⇒ l = 25 m.
Curved surface area = πrl
=
= 1885.71 m2
Given, 10% of canvas is used in folds and stitchings.
∴ = 188.571 m2.
Total area of canvas = 1885.71 + 188.571 = 2074.28 m2.
By formula,
⇒ Area of canvas = Length of canvas × Breadth of canvas
⇒ 2074.28 = Length × 1.5
Length = = 1382.85 m.
Given,
Cost of 1 m = ₹ 24
∴ Cost of 1382.85 m = 1382.85 × 24 = ₹ 33188.40.
Hence, length of canvas required = 1382.85 m and cost of canvas = ₹ 33188.40.
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