Diameter of a Cylinder

As we know, the radius of a cylinder is the radius of the 2 bases found at the top and the bottom of the cylinder. The diameter is then calculated by multiplying the radius by 2 as it is twice the radius. It is thus defined as the distance across a cylinder passing through the center. 

Similar to the radius, the units to calculate the diameter (d) are measured in units of length such as m, cm, mm, and ft. The diameter of the circle given is shown below.

Let us now learn how to find the diameter of a cylinder with formulas and solved examples.

Formula

The formula to calculate the diameter of a cylinder is derived from the formula used to find the volume of a cylinder as follows:

As we know,

Volume (V) = πr²h  

Rearranging the above equation in terms of r, we get

=> r² = V/πh

=> r = √(V/πh)

Multiplying both sides of the equation by 2, we get

=> 2 × r = 2√(V/πh)

=> d = 2√(V/πh) [∵ d = 2 × r]

Thus, the formula to calculate the diameter (d) of a cylinder is given as (d) = 2√(V/ πh)

Let us solve some examples to understand the concept better.

Solved Examples

Find the diameter of a cylinder having volume 1000 m³ and height 25 m.

Solution:

As we know,
d = 2√(V/πh), here V = 1000 m³, π = 3.141, h = 25 m
= 2√[1000/(3.141 × 25)]
= 2√(1000/78.525)
= 2√12.73
= 2 × 3.56
= 7.135 m

The volume of a cylinder is 2500 cm³ and the height is 75 cm. Calculate the diameter of the cylinder.

Solution:

As we know,
d = 2√V/πh, here V = 2500 cm³, π = 3.141, h = 75 cm
= 2√[2500/(3.141 × 75)]
= 2√(2500/235.575)
= 2√10.612
= 2 × 3.257
= 6.515 cm