Question : The lateral surface area of a frustum of a right circular cone, if the area of its base is 16$\pi$ cm2, the diameter of the circular upper surface is 4 cm and the slant height is 6 cm, will be:
Option 1: $30\pi$ cm2
Option 2: $48\pi$ cm2
Option 3: $36\pi$ cm2
Option 4: $60\pi$ cm2
Correct Answer: $36\pi$ cm 2
Solution :
Given: Upper diameter = 4 cm
Let the radius of the top surface be $r$.
$\therefore r = \frac{4}{2} = 2$ cm
Given that, the area of the base $=16\pi$
$⇒\pi R^2 = 16\pi$, where $R$ is the radius of base
$\therefore R = 4$ cm
The slant height of the frustum, $l$ = 6 cm
$\therefore$ Lateral surface area of the frustum $=\pi (R+r)l=\pi(4+2)\times6=36\pi$ cm
2
Hence, the correct answer is $36\pi$ cm
2
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