the radii of circular bases of a right circular cylinder and a cone are in the ratio of 3:4 and - Maths - Surface Areas and Volumes

Question

the radii of circular bases of a right circular cylinder and a
cone are in the ratio of 3:4 and their heights in the ratio 2:3
What is the ratio of their volumes?

Ankush Jain · Accepted Answer

Let the radius of circular base of cylinder be r₁ and the radius of circular base of cone be r₂

Given, $\frac{r_{1}}{r_{2}} = \frac{3}{4} ..... (1)$

||^gm, let the height of cylinder be h₁ and the height of cone be h₂.

Given, $\frac{h_{1}}{h_{2}} = \frac{2}{3} ..... (2)$

Now,

$\frac{Volume of cylinder}{Volume of cone} = \frac{π r_{1}^{2} h_{1}}{\frac{1}{3} π r_{2}^{2} h_{2}} = 3 (\frac{r_{1}}{r_{2}})^{2} (\frac{h_{1}}{h_{2}}) = 3 \times (\frac{3}{4})^{2} \times (\frac{2}{3}) = \frac{9}{16} \times 3 = \frac{9}{8}$

∴ Volume of cylinder : Volume of cone = 9:8.

the radii of circular bases of a right circular cylinder and a cone are in the ratio of 3:4 and their heights in the ratio 2:3 . What is the ratio of their volumes?