The radii of two right circular cylinders are in the ratio 2:3 and their heights are in the ratio 5:4 - Maths - Surface Areas and Volumes

Question

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

Priyanka Kedia · Accepted Answer

Let the radii and height of two right circular cylinders are $r_{1}, r_{2} a n d h_{1}, h_{2}$ respectively.

Given, radii of two right circular cylinders are in the ratio 2:3 and height are in the ratio 5:4.

Therefore,

$\frac{r_{1}}{r_{2}} = \frac{2}{3} a n d \frac{h_{1}}{h_{2}} = \frac{5}{4}$

So,

$\frac{C u r v e d S u r f a c e a r e a (S_{1})}{C u r v e d S u r f a c e a r e a (S_{2})} = \frac{2 π r_{1} h_{1}}{2 π r_{2} h_{2}} = (\frac{r_{1}}{r_{2}}) (\frac{h_{1}}{h_{2}}) = (\frac{2}{3}) (\frac{5}{4}) = \frac{5}{6} \Rightarrow \frac{C u r v e d S u r f a c e a r e a (S_{1})}{C u r v e d S u r f a c e a r e a (S_{2})} = \frac{5}{6}$

Thus, Surface area of right circular cylinders are in the ratio 5:6.

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