Question

The ratio of the curved surface area and the total surface area of a right circular cylinder is 5:7, find the ratio between the height and their radius

Answer 1

2πrh/2πr(r+h)=5/7

h/r+h=5/7

7h=5r+5h

7h-5h=5r

2h=5r

h/r=5/2

Answer 2

Given :

Ratio of curved surface area to total surface area = 5 : 7

To find : Ratio between the height and their radius.

Solution :

As we know that

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

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

So, it becomes :

Curved surface : Total surface area is given by:

$\dfrac{2\pi rh}{2\pi r(r+h)}=\dfrac{5}{7}\\\\\dfrac{h}{r+h}=\dfrac{5}{7}\\\\7h=5(r+h)\\\\7h=5r+5h\\\\7h-5h=5r\\\\2h=5r\\\\\dfrac{h}{r}=\dfrac{5}{2}$

Hence, the required ratio of height to their radius is 5:2.