Table of Contents

Last modified on April 25th, 2024

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.

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) = πr^{2}h

Rearranging the above equation in terms of r, we get

=> r^{2} = 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.

**Find the diameter of a cylinder having volume 1000 m ^{3 }and height 25 m.**

Solution:

As we know,

d = 2√(V/πh), here V = 1000 m^{3}, 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 cm ^{3 }and the height is 75 cm. Calculate the diameter of the cylinder.**

Solution:

As we know,

d = 2√V/πh, here V = 2500 cm^{3}, π = 3.141, h = 75 cm

= 2√[2500/(3.141 × 75)]

= 2√(2500/235.575)

= 2√10.612

= 2 × 3.257

= 6.515 cm

Last modified on April 25th, 2024

Good job

Correction done, it will be 3.257