Multiple choice

A dish in the shape of a frustum of a cone has a height of $6$cm. Its top and its bottom have radii of $24$cm and $16$cm respectively. Find its curved surface area. ( in $\displaystyle cm^{2}$)

  1. $200 \displaystyle \pi $
  2. $300 \displaystyle \pi $
  3. $400 \displaystyle \pi $
  4. $500 \displaystyle \pi $
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C Correct answer
Explanation

The slant height l = sqrt(h^2 + (R-r)^2) = sqrt(6^2 + (24-16)^2) = sqrt(36 + 64) = 10. The curved surface area of a frustum is pi * (R+r) * l = pi * (24+16) * 10 = 400 * pi.

AI explanation

To find the curved surface area of a frustum, we first determine its slant height using the Pythagorean theorem, which is sqrt(6^2 + (24 - 16)^2) = 10 cm. The curved surface area formula is pi * (R + r) * l. Substituting the values gives pi * (24 + 16) * 10, which equals 400 * pi square centimeters. The curved surface area is 400 pi.

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