Question
A right circular cone has a slant height of 30 cm and
its curved surface area is 1,320 cm². A cylindrical vessel has radius 25% more than the cone’s radius, and height 25 cm. If the top of the cylinder is open, find the total cost of painting the outside at Rs. 3 per cm². (Use π = 22/7)Solution
ATQ,
ATQ: Curved surface area of cone = π × radius × slant height ⇒ (22/7) × radius × 30 = 1,320 ⇒ radius = 14 cm Radius of cylinder = 1.25 × 14 = 17.5 cm Required area of cylinder = CSA + base area (top is open) = 2 × π × radius × height + π × radius² = 2 × (22/7) × 17.5 × 25 + (22/7) × (17.5)² = 2,750 + 962.5 = 3,712.5 cm² Therefore, cost of painting = 3,712.5 × 3 = Rs. 11,137.50
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