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Question

The radii of the ends of a frustum of a right circular cone are 5 metres and 8 metres and its lateral height is 5 metres. Find the lateral surface area and volume of the frustum.

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Solution

Given, radii of the ends of a frustum are r=5 m and R=8 m
Lateral height l=5 m
LSA of frusturn=π(R+r)l
=227(8+5)×5 m2
=204.29 m2

Height h=l2(Rr)2
=52(85)2 m
=16 m
=4 m
Volume of the frustum =13πh(R2+r2+Rr)
=13×227×4(82+52+8×5)
=13×227×4×129
=540.57 m2

Hence, the lateral surface area is 204.29 m2 and volume is 540.57 m2.

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