A tent of height 8.25 m is in the form of a right circular cylinder with diameter of base 30 m and height 5.5 m, surmounted by a right circular cone of the same base. Find the cost of the canvas of the tent at the rate of Rs 45 per m².
Answers
Answer:
The cost of canvas is ₹ ₹ 55,687.5
Step-by-step explanation:
SOLUTION :
Given
Diameter of the cylinder = 30 m
Radius of the cylinder , r = 30 / 2 m = 15 m
Height of the tent = 8.25 m
Height of the cylindrical part ,H = 5.5 m
Height of the right circular cone , h = (8.25 – 5.5) = 2.75 m
Let the slant height of the cone be (l).
l = √r² + h²
l = √(15)² + (2.75)²
l = √225 + 7.5625
l = √232.5625
l = 15.25
slant height of the cone is 15.25 m.
Total curved surface area of the tent = Curved surface area of the cylinder + Curved surface area of the cone
= 2πrh + πrl
= πr(2h + l)
= π ×15 × (2 × 5.5 + 15.25)
= π × 15(11 + 15.25)
= 22/7 × 15 × 26.25
= 22 × 15 × 3.75
Total curved surface area of the tent = 1,237.5 m²
Rate of canvas = ₹ 45 per m²
Cost of canvas of tent = 1,237.5 m² × ₹ 45 = ₹ 55,687.5
Cost of canvas of tent = ₹ 55,687.5
Hence, the cost of canvas is ₹ ₹ 55,687.5
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Step-by-step explanation:
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