Multiple choice

A frustum of a right circular cone is of height $16$ cm with radii of its ends as $8$ cm and $20$ cm has lateral surface area equal to

  1. $540\, \pi\, cm^{2}$
  2. $580\, \pi\, cm^{2}$
  3. $560\, \pi\, cm^{2}$
  4. $680\, \pi\, cm^{2}$
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C Correct answer
Explanation

Lateral surface area of a frustum = pi * (R + r) * l. Slant height l = sqrt(h^2 + (R - r)^2) = sqrt(16^2 + (20 - 8)^2) = sqrt(256 + 144) = 20. Area = pi * (20 + 8) * 20 = 560 * pi.

AI explanation

The lateral surface area of a frustum of a cone is calculated using the formula pi times the sum of the two radii times the slant height. First, use the Pythagorean theorem to find the slant height, which is the square root of the difference of the radii squared plus the height squared: the square root of 12 squared plus 16 squared, yielding 20 centimeters. Substituting the values into the area formula gives pi times 28 times 20, resulting in an area of 560 times pi square centimeters.

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