Question

The radii of two right circular cylinders are in the ratio 2:3 and their heights are in the

ratio 3:4. Calculate the ratio of their volumes.​

Answer 1

Answer:

Let the radii of the two right circular cylinders be $\sf{r}_{1}$ & $\sf{r}_{2}$ and height be $\sf{h}_{1}$ & $\sf{h}_{2}$.

Given -

$\\ \sf \: \frac{r_1}{r_2} = \frac{2}{3}$

and

$\\ \sf \: \frac{h_1}{h_2} = \frac{3}{4}$

Now, let's find the ratio of their volumes -

$\\ \sf \: \frac{\pi_1 {}^{2}h_1 }{\pi_2 {}^{2} h_2} = { \bigg( \frac{r_1}{r_2} \bigg)}^{2} \bigg( \frac{h_1}{h_2} \bigg)$

Now, by putting the given values -

$\\ \implies \sf \: { \bigg( \frac{2}{3} \bigg)}^{2} \bigg( \frac{3}{4} \bigg) \\ \\ \implies \sf \: \frac{4}{9} \times \frac{5}{3} \\ \\ \\ \implies \sf \blue{20 \ratio \: 27}$

The ratio of their volumes is 20 : 27.

Answer 2

Answer:

ratio of their volumes=1:3

Step-by-step explanation:

VOLUME OF CYLINDER = π$r^{2}$h

let their radii be 2r and 3r and their height be 3h and 4h respectively.

vol. of first cylinder= $\pi$$(2r)^{2}3h=\pi 4r^{2}*3h=12\pi r^{2} h$

vol of second cylinder=$\pi (3r)^{2} 4h=\pi 9r^{2}*4h=36\pi r^{2} h$

ratio of their volumes=$\frac{12\pi r^{2}h }{36\pi r^{2}h} =\frac{1}{3}=1:3$