Volume of a Cone (Exact and Approximate)

Exact: \(32\pi\) ft³   Approx: ≈ 100.53 ft³

Explanation

\[V = \frac{1}{3}\pi r^2 h\]

This is the formula for the volume of a cone.

\[V = \frac{1}{3}\pi(4)^2(6)\]

Substitute 4 for \(r\), the radius of the base, and 6 for \(h\), the height.

\[= \frac{1}{3}\pi(16)(6)\]

Evaluate the exponential expression: \((4)^2 = 16\).

\[= 2\pi(16)\]

Multiply: \(\frac{1}{3}(6) = 2\).

\[= 32\pi\]

Multiply: \(2(16) = 32\). Write the product so that \(\pi\) is the last factor.

\[\approx 100.53 \text{ ft}^3\]

Use a calculator. The exact volume of the cone is \(32\pi\) ft³. To the nearest hundredth, the volume is 100.53 ft³.