Question
The radius of a cone matches the
radius of a circle with an area of 1386 cm². The slant height of the cone is twice the length of a rectangle with an area of 84 cm² and a breadth of 7 cm. Calculate the lateral surface area of the cone.Solution
ATQ, The area of the circle =1386 cm2 π × r2 = 1386 22/7 × r2 = 1386 r = √(1386 × (7 /22)) r= √(63×7) = √441 = 21 cm Area of the rectangle = l × b 84 = l × 7 l = 12 length of the rectangle = 12 cm Slant height of the cone = 2 × 12 = 24 Lateral surface area of the cone = π × r × l cm2 = 22/7 × 21 × 24 = 22× 3 × 24 = 1584 cm2
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