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How to Find the Diameter of a Cylinder?

TopCylinder is a solid shape body, which is rounded at the top and bottom. The shape at the top and bottom are circular. A cylinder mainly consists of radius, diameter and height. We can find the diameter of any cylinder, if we have the volume of the cylinder. We know that the radius of the circle is just half of the diameter. So, if we find the radius, then we need to just double it.

For finding radius, we need to have one of the three parameters: volume, total surface area or circumference of the cylinder.
  1. If we have circumference, then we can find the radius by a simple formula as circumference = $2 \pi r$. And, when we get the radius, we can easily find the diameter by doubling it. 
  2. If we have the total surface and height, then we can find the radius by the formula, total surface area = $2 \pi r (h + r)$.
  3. If we have volume, then we can find the diameter of the cylinder by a simple calculation. We know that the volume of a cylinder is $\pi r^2 h$. So, with volume, we also need height to find the diameter.

Now we will see an example in which we will find the diameter of a cylinder.

Example:

If the volume of a cylinder is 33 inch, and height is 7 inch, then find the diameter of the cylinder.

Solution:

Volume of a cylinder = $\pi r^2 h$
So, according to the question.

$33$ = $\frac{22}{7}$$ \times r^2 \times 7$

$r^2$ = $\frac{22}{7}$$ \times $$\frac{7}{33}$

$r^2$ = $\frac{2}{3}$

r = $\sqrt{\frac{2}{3}}$ inch.

Diameter = 2$\sqrt{\frac{2}{3}}$ inch..