10.01 Volume of cylinders

We have already seen how the volume of rectangular prisms can be calculated using the formula \text{Volume} = \text{Area of Base} \times \text{Height of Prism}

A cylinder is very similar to a prism, except that the base is a circle instead of a rectangle or other polygon, but the volume can be found using the same process.

\begin{aligned} \text{Volume of Cylinder} &= \text{Area of Base} \times \text{Height of Prism}\\ &=\pi \times r^2 \times h \\ &=\pi r^2 h \end{aligned}

Examples

Example 1

Find the volume of a cylinder correct to one decimal place if its radius is 5\text{ cm} and its height is 13\text{ cm.}

Worked Solution

Create a strategy

Use the formula of the volume of a cylinder.

Apply the idea

We have been given values for r=5 and h=13 into the formula.

\displaystyle V	\displaystyle =	\displaystyle \pi r^2 h	Use the formula
	\displaystyle =	\displaystyle (\pi \times 5^2) \times 13	Substitute the values
	\displaystyle =	\displaystyle \pi \times 25 \times 13	Evaluate the squares
	\displaystyle =	\displaystyle 1021.0\, \text{cm}^3	Evaluate

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Example 2

Consider the halfpipe with a diameter of 7\text{ cm} and a height of 16\text{ cm.}

Find its volume, rounding to two decimal places.

Worked Solution

Create a strategy

Use the fact that the volume of the halfpipe is half of the volume of the cylinder, and the radius is half of the diameter.

Apply the idea

We have been given the values for diameter of\,7\,\text{cm} and height of \,16\,\text{cm} .

Since the radius is half of the diameter, then r=\dfrac{7}{2}.

\displaystyle V	\displaystyle =	\displaystyle \dfrac{1}{2} \times \pi r^2 h	Multiply the cylinder formula by a half
	\displaystyle =	\displaystyle \dfrac{1}{2} \times \pi \times \left(\dfrac{7}{2}\right)^2\times 16	Substitute the values
	\displaystyle =	\displaystyle 307.88\, \text{cm}^3	Evaluate the product