If the ratio between the curved surface area and the total surface area of a right circular cylinder is $3 : 4$ , find the ratio of height to the radius of the cylinder.

Open in App

Solution

$\frac{C . S . A}{T . S . A} = \frac{2 π r h}{2 π r (r + h)} = \frac{3}{4}$

$\Rightarrow \frac{h}{r + h} = \frac{3}{4}$

$\Rightarrow 4 h = 3 r + 3 h$
$\Rightarrow h = 3 r$
$\Rightarrow \frac{h}{r} = 3$

Suggest Corrections

Similar questions

Q. Ratio between the curved surface area and the total surface area of a right circular cylinder is 1:2. Ratio between height and radius of cylinder is .

Question 119

The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2. Find the ratio between the height and radius of the cylinder.

Q. The ratio between the curved surface area and the total surface area of a right circular cylider is 1:2. Find the ratio between the height and radius of the cylinder.

Q. If the ratio of curved surface area and total surface area of a cylinder is 1 : 4, find the ratio of radius and height of the cylinder.

Q. The ratio of the curved surface area to the total surface area of a right circular cylinder is 1 : 2. The ratio of the height to the radius of the cylinder is _____.

Join BYJU'S Learning Program

If the ratio between the curved surface area and the total surface area of a right circular cylinder is 3:4, find the ratio of height to the radius of the cylinder.

C.S.AT.S.A=2πrh2πr(r+h)=34 ⇒hr+h=34 ⇒4h=3r+3h ⇒h=3r ⇒hr=3

If the ratio between the curved surface area and the total surface area of a right circular cylinder is $3 : 4$ , find the ratio of height to the radius of the cylinder.

$\frac{C . S . A}{T . S . A} = \frac{2 π r h}{2 π r (r + h)} = \frac{3}{4}$

$\Rightarrow \frac{h}{r + h} = \frac{3}{4}$

$\Rightarrow 4 h = 3 r + 3 h$
$\Rightarrow h = 3 r$
$\Rightarrow \frac{h}{r} = 3$