The cost of the canvas required to make a conical tent of base radius 8 m at the rate of Rs. 40 per m2 is Rs. 10,048. Find the height of the tent (Take π=3.14).
8 m
7 m
6 m
10 m
A
10 m
B
6 m
C
8 m
D
7 m
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Solution
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To find the amount of canvas required to make a conical tent, we need to calculate the lateral surface area of the tent.
Lateral surface area of a cone of radius r, height h=πr√h2+r2.
As the total cost to make the tent is Rs. 10048 at the rate of Rs. 40per m2,
the total area Lateral surface area =Total cost of canvasCost of canvas per m2
=1004840=251.2m2.
So, lateral surface area:
πr×√h2+r2=251.2 ⇒3.14×8×√h2+82=251.2 ⇒√h2+82=10
Squaring both sides, we get: h2+64=100 ⇒h2=36 ⇒h=6m
Hence, option A is correct.
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