2025 · Q51
Consider the following for the next two (02) items that follow: A frustum of a right cone has a top of diameter 2k, bottom of diameter 2.5k and height k. What is the whole surface area of the frustum?
Elementary MathematicsMensuration
- A39πk²/8
- B41πk²/8
- C43πk²/8
- D45πk²/8
Explanation
With top radius k, bottom radius 1.25k and height k, the slant height is l = √(k² + (k/4)²) = k√17/4. The total surface area is π(R+r)l + πR² + πr² = πk²(9√17 + 41)/16 ≈ 4.88πk². Among the options this is closest to 39πk²/8 = 4.875πk², option (a).