Volume of a Cylinder (Exact and Approximate)

Exact: \(90\pi\) cm³   Approx: ≈ 282.74 cm³

Explanation

Since a radius is one-half of the diameter of the circular base, \(r = \frac{1}{2}(6 \text{ cm}) = 3 \text{ cm}\). From the figure, the height of the cylinder is 10 cm. To find the volume of the cylinder:

\[V = \pi r^2 h\]

This is the formula for the volume of a cylinder.

\[V = \pi (3)^2 (10)\]

Substitute 3 for \(r\), the radius of the base, and 10 for \(h\), the height.

\[= \pi(9)(10)\]

Evaluate the exponential expression: \((3)^2 = 9\).

\[= 90\pi\]

Multiply: \((9)(10) = 90\). Write the product so that \(\pi\) is the last factor.

\[\approx 282.74 \text{ cm}^3\]

Use a calculator. The exact volume of the cylinder is \(90\pi\) cm³. To the nearest hundredth, the volume is 282.74 cm³.