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The slant height of a frustum of a cone is $4$ cm and the perimeters $( circumferences)$ of its ends are $18$ cm and $6$ cm. Find the curved surface area of the frustum.
Given: A frustum with a slant height l=4 cm and the circumference of its ends R$=18$ cm and r$=6$ cm.
To do: To find out the curved surface area of the frustum.
Solution:
Here we draw a frustum that has a slant height l and radius of both circular ends are R and r.
Here given slant height $l=4$ cm
Perimeter of upper circular end $= 2\pi\ R=18$ cm
$\Rightarrow \pi\ R=18/2=9$
And perimeter of lower circular end $=2\pi\ r=6$
$\Rightarrow \pi r=6/2=3$
As known the surface area of a frustum with slant height l and radius R and r of both.
Circular ends $A=\pi\ l( r+R)$
$\Rightarrow A=( \pi\ r+\pi\ R)$
By putting the value of $\pi\ r=9$ and $\pi\ R=3$
$A=( 9+3)4=48$
Thus the surface area of the frustum is $48\ cm^{2}$.
Updated on: 10-Oct-2022
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