Find the curved surface area of the frustrum in the figure
 

  • A 16\(\pi \sqrt{10}\)cm²
  • B 20\(\pi \sqrt{10}\)cm²
  • C 24\(\pi \sqrt{10}\)cm²
  • D 36\(\pi \sqrt{10}\)cm²
jamb 1990mathematics

The correct answer is B. 20\(\pi \sqrt{10}\)cm²

\(\frac{x}{4} = \frac{6 + x}{6}\)
6x = 4(6 + x) = 24 + 4x
x = 12cm 
 CSA = \(\pi RL - \pi rl\)
= \(\pi (6) \sqrt{{18^2} + 6^2} - \pi \times 4 \times \sqrt{{12^2} + 4^2}\)
= 6\(\pi \sqrt{360} - 4 \pi \sqrt{160}\)
= 36\(\pi \sqrt{10} - 16 \pi \sqrt{10}\)
= 20\(\pi \sqrt{10}\)cm2

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