Radius of a Cone

The radius of a cone is the radius of its circular base. It is the distance between the center of the circular base to any point on its circumference. It is denoted by r.

Since it is a linear parameter, it is expressed in mm, cm, m, in, ft, or yd.

Formula

The formula to calculate the radius of a cone can be obtained from the formula used to calculate the volume of a cone.

As we know,

Volume ${\left( V\right) =\dfrac{1}{3}\pi r^{2}h}$, here r = radius, h = height, π = 3.141

Therefore, after rearranging the equation, we get:

∴ Radius ${\left( r\right) =\sqrt{\dfrac{3V}{\pi h}}}$

Solved Examples

Find the radius of a cone with a volume of 268.1 cm² and a height of 16 cm.

Solution:

As we know,
Radius ${\left( r\right) =\sqrt{\dfrac{3V}{\pi h}}}$, here V = 268.1 cm², h = 16 cm
${= \sqrt{\dfrac{3\times 268\cdot 1}{3\cdot 141\times 16}}}$
= 4 cm

Calculate the radius of a right circular cone whose height is 11 mm and slant height is 8 mm.

Solution:

Here we will apply the Pythagorean’s Theorem considering the slant height as hypotenuse and height as the perpendicular leg and find out the radius as the base of a right triangle.
Radius ${\left( r\right) =\sqrt{s^{2}-h^{2}}}$, here s = 11 mm, h = 8 mm
${\therefore r=\sqrt{11^{2}-8^{2}}}$
= 7.55 mm