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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 and volume of the frustum.
Solution
Lateral surface area of frustum
\[= \pi\left( r + R \right)l\]
\[ = \pi\left( 5 + 8 \right) \times 5\]
\[ = 204 . 28 m^2\]
Height of cone
`h = sqrt(5^2 - (R -r)^2)`
`=sqrt(5^2 - (8-5)^2)`
`=sqrt13`
Volume `=(pi xx sqrt13)/3 (8^2 + 5^2 + 40) = 540.56 cm^3`.
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