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Question
A bucket is in the form of a frustum of a cone and holds 28.490 litres of water . The radii of the top and bottom are 28 cm and 21 cm respectively . Find the height of the bucket .
Solution
Radii r1 = 21 cm and r2 = 28 cm
Let the height of the bucket be h.
Volume of the bucket which is in the form of the frustum
\[V = \frac{1}{3}\pi h\left( r_1^2 + r_1 r_2 + r_2^2 \right)\]
\[ \Rightarrow \frac{1}{3}\pi h\left( {28}^2 + 28 \times 21 + {21}^2 \right) = 28490\]
\[ \Rightarrow h = 14 . 9 \approx 15 cm\]
Hence, the height of the bucket is 15 cm.
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