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Frustum of a Cone

A vessel is i...

Question

A vessel is in the form of a frustum of a cone. Its radius at top end is $10$ m and the bottom end is $5$ m. Its volume is $402 π$ cubic meter. Find its height.

A

5.68

m

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B

6.89

m

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C

7.21

m

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D

8.34

m

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Solution

The correct option is B $6.89$ m
Volume of a frustum cone $= π \times \frac{h}{3} (R^{2} + R r + r^{2})$
$402 = π \times \frac{h}{3} (10^{2} + 50 + 5^{2})$
$402 \times 3 = h (100 + 50 + 25)$
$1, 206 = h (175)$
$h = 6.89$ m

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