A tent is in the form of a cylinder of diameter 20 m and height 2.5 m, surmounted by a cone of equal base and height 7.5 m. find the capacity of the tent and the cost of the canvas at Rs. 100 per square metre.
Answers
Step-by-step explanation:
Radius of the cylinder = Radius of the cone ,r = 10 m
Height of the cylinder , H = 2.5 m
Height of the Cone , h =7.5 m
Slant height of the cone , l = √r² + h²
l = √10² + 7.5² = √100 + 56.25 = √156.25
l = 12.5 m
Capacity of the tent = Volume of cylinder + volume of cone
= πr²H + ⅓ × πr²h
= πr²(H + ⅓ × h)
= π × 10² (2.5 + ⅓ × 7.5)
= 100π (2.5 + 2.5)
= 100 π × 5 = 500 π
V1 = 500 π m³.
capacity of the tent = 500 π m³.
Total area of the canvas required for the tent ,S = curved surface area of cylinder + curved surface area of cone
S = 2πrH + πrl
S = 2(π)(10)(2.5) + π(10)(12.5)
S = 50π + 125π
S = π(50 + 125) = π × 175 = 22/7 × 175 = 22 × 25
S = 550 m²
Total cost of the canvas = Total area of the canvas × Rate
= (100) (550) = ₹ 55000
Total cost of the canvas = ₹ 55000
Hence, Total capacity of the tent = 500 π m³ & Total cost of the canvas is ₹ 55000.
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