UPSKILL MATH PLUS

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### 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.

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

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

$$=$$ $\frac{22}{7}×28×14$

$$=$$ $$22 \times 4 \times 14$$

$$=$$ $$1232$$

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.