UPSKILL MATH PLUS

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Learn more### Theory:

Hollow cylinder:

A cylinder emptied from the inner side and has a difference in the outer and inner radius of a cylinder with the same height is called a hollow cylinder.

Volume of a hollow cylinder:

Let \(R\) be the outer radius, \(r\) be the inner radius, and \(h\) be the height of the hollow cylinder.

Volume \(=\) Volume of the outer cylinder \(-\) Volume of the inner cylinder

\(=\) \(\pi R^2 h - \pi r^2 h\)

\(=\) \(\pi (R^2 - r^2) h\)

Volume of a hollow cylinder \(=\) \(\pi (R^2 - r^2) h\) cu. units.

Example:

Find the volume of the hollow cylinder of height \(14\) \(cm\) and whose internal and external radii are \(6\) \(cm\) and \(8\) \(cm\), respectively.

**Solution**:

Internal radius, \(r\) \(=\) \(6\) \(cm\)

External radius, \(R\) \(=\) \(8\) \(cm\)

Height, \(h\) \(=\) \(14\) \(cm\)

Volume of a hollow cylinder \(=\) \(\pi (R^2 - r^2) h\) cu. units.

\(=\) $\frac{22}{7}\times \left({8}^{2}-{6}^{2}\right)\times 14$

\(=\) $\frac{22}{7}\times \left(64-36\right)\times 14$

\(=\) $\frac{22}{7}\times 28\times 14$

\(=\) \(22 \times 4 \times 14\)

\(=\) \(1232\)

Therefore, the volume of a hollow cylinder is \(1232\) \(cm^3\).

Important!

The value of \(\pi\) should be taken as $\frac{22}{7}$ unless its value is shared in the problem.