Find the curved surface area of the frustrum in the figure
Attached Figure / Diagram
A
16\(\pi \sqrt{10}\)cm2
B
20\(\pi \sqrt{10}\)cm2
C
24\(\pi \sqrt{10}\)cm2
D
36\(\pi \sqrt{10}\)cm2
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(\frac{x}{4} = \frac{6 + x}{6}\)
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
Source: Myschool Past Questions Archive (Record #32962)