Multiple choice

Curved surface area of a cone whose radius is 21 cm is 1914 cm2. If height of cone is half than that of perimeter of a square, then find the area of square?

  1. 36 cm2

  2. 196 cm2

  3. 100 cm2

  4. 64 cm2

  5. 144 cm2
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C Correct answer
Explanation

The curved surface area of a cone is pi*r*l = 1914. With r=21, l = 1914 / (22/7 * 21) = 29. Using the Pythagorean theorem, the height h = sqrt(l^2 - r^2) = sqrt(29^2 - 21^2) = sqrt(841 - 441) = 20. Since the height is half the perimeter of the square, the perimeter is 40, meaning each side is 10. The area of the square is 10^2 = 100.

AI explanation

The lateral surface area of a cone equals pi times radius times slant height, so 1914 equals 22 over 7 times 21 times slant height, yielding a slant height of 29 cm. Using the Pythagorean theorem, the height of the cone is the square root of 29 squared minus 21 squared, which is 20 cm. Because this height is half the perimeter of the square, the perimeter of the square is 40 cm, making its side length 10 cm and its area 100 square cm.

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