A tent is of the shape of a right circular cylinder upto a height of 3 metres and then becomes a right circular cone with a maximum height of 13.5 metres above the ground. Calculate the cost of painting the inner side of the tent at the rate of Rs 2 per square metre, if the radius of the base is 14 metres.
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Answer:
The Cost of painting the inner side of the tent is ₹ 2068 .
Step-by-step explanation:
SOLUTION :
Given :
Radius of the cylinder and cone, r = 14 cm
Height of a cylinder, h = 3 m
Total height of the tent = 13.5 m
Height of the conical part, H = 13.5 - 3 = 10.5 m
Slant height of the cone, l = √r² + H²
l = √14² + 10.5²
l = √196 + 110.25
l = √306.26
l = 17.5 m
Slant height of the cone, l = 17.5 m
Area of inner side of the tent = curved surface area of cone + curved surface area of the cylinder
= πrl + 2πrh
= πr(l + 2h)
= π× 14(17.5 + 2 × 3)
= 14π (17.5 + 6)
= 14π (23.5)
= 14 × 22/7 × 23.5
= 44 × 23.5
= 1034 m²
Area of inner side of the tent = 1034 m²
Rate of painting the inner side of the tent = ₹ 2 per m²
Cost of painting the inner side of the tent = 1034 × 2 = ₹ 2068
Hence, the Cost of painting the inner side of the tent is ₹ 2068 .
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