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 . 

Answer 1

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.