The radius of two cylinders are in the ratio 2 : 3 and their heights

1.	The radius of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. Calculate the ratio of their volumes.
Answer» Given, Ratio of radius of two cylinder = 2 : 3 = \(\frac{r_1}{r_2}\) = \(\frac{2}{3}\) Ratio of their heights = 5 : 3 = \(\frac{volume\,of\,cylinder\,1}{volume\,of\,cylinder\,2}\) = \(\frac{πr^2_1h_1}{πr^2_2h_2}\) = \(\frac{4\times 5}{9\times 3}\) = \(\frac{20}{27}\) ∴ Ratio of volumes of two cylinder = 20 : 27

The radius of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. Calculate the ratio of their volumes.

Answer»

Given,

Ratio of radius of two cylinder = 2 : 3

= \(\frac{r_1}{r_2}\) = \(\frac{2}{3}\)

Ratio of their heights = 5 : 3

= \(\frac{volume\,of\,cylinder\,1}{volume\,of\,cylinder\,2}\) = \(\frac{πr^2_1h_1}{πr^2_2h_2}\) = \(\frac{4\times 5}{9\times 3}\) = \(\frac{20}{27}\)

∴ Ratio of volumes of two cylinder = 20 : 27