Find the ratio between the total surface area of a cylinder to its curved surface area, given that its height and radius are $7.5\ cm$ and $3.5\ cm$.

Given:

The height and radius of a cylinder are $7.5\ cm$ and $3.5\ cm$ respectively.

To do:

We have to find the ratio between the total surface area to its curved surface area.

Solution:

Radius of the cylinder $(r) = 3.5\ cm$

Height of the cylinder $(h) = 7.5\ cm$

This implies,

Total surface area of the cylinder $= 2 \pi r (h + r)$

Curved surface area of the cylinder $= 2 \pi rh$

Therefore,

Ratio $=\frac{2 \pi r(h+r)}{2 \pi r h}$

$=\frac{h+r}{h}$

$=\frac{7.5+3.5}{7.5}$

$=\frac{11}{7.5}$

$=\frac{110}{75}$

$=\frac{22}{15}$

The required ratio is $22: 15$.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

48 Views

Kickstart Your Career

Get certified by completing the course

Get Started