Volume of a Spherical Water Tank

Exact: \(4{,}500\pi\) ft³   Approx: ≈ 14,137.2 ft³

Explanation

\[V = \frac{4}{3}\pi r^3\]

This is the formula for the volume of a sphere.

\[V = \frac{4}{3}\pi(15)^3\]

Substitute 15 for \(r\), the radius of the sphere.

\[= \frac{4}{3}\pi(3{,}375)\]

Evaluate the exponential expression: \((15)^3 = 3{,}375\).

\[= \frac{13{,}500}{3}\pi\]

Multiply: \(4(3{,}375) = 13{,}500\).

\[= 4{,}500\pi\]

Divide: \(\frac{13{,}500}{3} = 4{,}500\). Write the product so that \(\pi\) is the last factor.

\[\approx 14{,}137.2 \text{ ft}^3\]

Use a calculator. The tank holds exactly \(4{,}500\pi\) ft³ of water. To the nearest tenth, this is 14,137.2 ft³.