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Question

The slant height of a frustum of a cone is $$4\ cm$$ and the perimeters (circumference) of its circular ends are $$18\ cm$$ and $$6\ cm$$. Find the curved surface area of the frustum.


Solution

Given:
$$l=4$$ cm

Circumference of  a circular end =$$18$$ cm
$$\Rightarrow 2\pi r_1=18$$
$$\Rightarrow \pi \times r_1=\dfrac{18}{2} =9$$ ...............................(1)

Circumference of other circular end  $$=6 $$ cm
$$\Rightarrow 2\pi r_2=6$$
$$\Rightarrow \pi r_2=\dfrac{6}{2}=3$$..........................................(2)

Adding (1) and (2)
Curved surface area 
$$=\pi (r_1+r_2) l$$
$$=(9+3) \times 4$$
$$=48$$ cm$$^2$$

497652_465194_ans.png

Mathematics
RS Agarwal
Standard X

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