Question

A farmer built a granary in the shape of a cylinder to store his crop . The capacity of the granary is 768 pi r ft of power 3 and the radius of its circular base is 8 ft .The farmer want to builds another granary of the same volume but with half the radius of the circular base ,then the height of the new granary will be ?

Answer 1

Answer :

Given : The capacity of the granary is 768 $\mathrm{\pi }$ ft³ and the radius of its circular base is 8 ft .
And
The farmer want to builds another granary of the same volume but with half the radius of the circular base . So

Radius of new granary = 4 ft
And
Let height of granary = h

We know Volume of cylinder = $\pi r^{2}h$ , So

$$\begin{gathered} \pi r^{2}h=768\pi \\ \Rightarrow \pi \times 4^2\times h=768\pi \\ \Rightarrow 16h=768 \\ \Rightarrow h=\frac{768}{16} \\ \Rightarrow h=48 \end{gathered}$$
So,

Height of new granary = 48 ft ( Ans )