Question

A cone and cylinder are having the same base. Find the ratio of their height if their volume are equal.

Answer 1

answer is 2:5..............

Answer 2

AnswEr:

Let the radius of the common base be r. Let $\sf{h}_{1}$ and $\sf{h}_{2}$ be the heights of the cone and cylinder respectively. Then,

• Volume of the cone = $\sf\dfrac{1}{3}\pi\:r^2\:h_1$

• Volume of the cylinder = $\sf{\pi\:r^2\:h_2}$

________________________________________

• It is given that the cone and cylinder are of the same volume.

$\therefore \sf \frac{1}{3} \: \pi {r}^{2}h_1 = \pi {r}^{2} h_2 \rightarrow \: \frac{1}{3} \: h_1 = h_2 \\ \\ \implies \sf \frac{h_1}{h_2} = \frac{3}{1} \\ \\ \rightarrow \sf \: h_1 \colon h_2 \: = 3 \colon 1$