Question

The radii of two right circular cylinders are in the ratio of 2 : 3 and their heights are in the ratio of 5 : 4. Calculate the ratio of their curved surface areas and ratio of their volumes

Answer 1

2$\pi$rh/2$\pi$r1h1
2.2x.5x.$\pi$/2.3x.4x.$\pi$
10/12
5/6=5:6 ratio of csa
ratio of volume=
20/36=5/9=5:9=ratio of volume

Answer 2

Let the radius of first cylinder be r

1 and height be h1 and let the radius of second cylinder be r2 and height be h2

Then according to question

$\frac{ r_{1}}{r_{2}} = \frac{2}{3} \: \: and \: \: \frac{h_{1}}{h_{2}} = \frac{5}{4}$

Curved surface area of first cylinder S1=

$2\pi r_{1}h_{1}$

and curved surface area of second cylinder S2=

$2\pi r_{2}h_{2}$

$∴ \frac{S_{1}}{S_{2}}= \frac{2\pi r_{1}h_{1}}{2\pi r_{2}h_{2}}$

$= (\frac{r_{1}}{r_{2}} ) ( \frac{h_{1}}{h_{2}} )$

$= (\frac{2}{3})( \frac{5}{4})$

$= \frac{5}{6}$

$S_{1}:S_{2} = 5:6$

The ratio of their volume

$\frac{V_{1}}{V_{2}} = \frac{ \pi {r}^{2}_{1}h_{1}}{ \pi {r}^{2}_{2}h_{1}}$

$=( \frac{2}{3} {)}^{2} •( \frac{5}{4} )$

$= \frac{4}{9} \times \frac{5}{4}$

$= \frac{5}{9}$

$∴V_{1}:V_{2} = 5:9$

Hence, ratio of curved surface area =5:6 and ratio of volumes =5:9