A military tent of height 10 m is in the form of a right circular cylinder with a diameter of base 24 m
and height 5.00 m surmounted by a right circular cone of same base radius. Find the cost of canvas
used in making the tent at RS 42 per sq. m.
and height 5.00 m surmounted by a right circular cone of same base radius. Find the cost of canvas
used in making the tent at RS 42 per sq. m.
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Step-by-step explanation:
Height of the cylinder (h1) = 5 m
Diameter of the cylinder (d1) = 24 m
So, the radius of the cylinder (r1) = 12 m
Since, height of the tent = 10 m
∴ Height of cone (h2) = 10 m – (height of cylinder) = (10 – 5) m = 5 m
∴ Slant height (l) of the cone can be calculated as
l2 = (12)2 + (5)2
⇒ l2 = 144 + 25
⇒ l2 = 169
⇒ l = 13 m
Now,
Total canvas used = curved surface area of cylinder + curved surface area of cone
= 2 πr1h1 + πr2l
= (377.143 + 490.286) m2
= 867.429 m2
Given that cost of canvas = Rs 42 per m2
∴ Total cost of canvas used in making the tent = Rs (867.429 × 42)
= Rs. 36431 (approx)