Let's Practice
You use the formula \(V=\frac{4}{3} \pi r^3\) to calculate the volume of a sphere. In this formula, \(V\) represents the volume, and \(r\) is the sphere's radius (the distance from the center to any point on the surface). The symbol \(\pi\) represents the number pi.
Use the activity below to practice calculating the volume of a sphere. Answer the question on each tab, then check your answer.
A sphere has a radius of \(5\) cm. What is the volume of the sphere? Round your final answer to the nearest hundredth.
\(V \approx 166.67 \pi \text{cm}^3\)
If you need help arriving at this answer, click the Solution button.
Step 1: Substitute the radius into the volume equation. |
\(V=\frac{4}{3} \pi r^3\) \(V=\frac{4}{3} \pi(5)^3\) |
Step 2: Cube the radius. |
\(V=\frac{4}{3} \pi(5)(5)(5)\) \(V=\frac{4}{3} \pi(125)\) |
Step 3: Simplify. Round your final answer to the nearest hundredth. Leave pi as the symbol \(\pi\). |
\(V=\frac{500}{3} \pi\) \(V \approx 166.67 \pi\ \text{cm}^3\) Remember that you need to label your answer with the unit given in the problem statement. |
A sphere has a radius of 6 feet. What is the volume of the sphere?
\(V=288 \pi\ \text{ft}^3\)
If you need help arriving at this answer, click the Solution button.
Step 1: Substitute the radius into the volume equation. |
\(V=\frac{4}{3} \pi r^3\) \(V=\frac{4}{3} \pi(6)^3\) |
Step 2: Cube the radius. |
\(V=\frac{4}{3} \pi(6)(6)(6)\) \(V=\frac{4}{3} \pi(216)\) |
Step 3: Simplify. Leave pi as the symbol \(\pi\). |
\(V=\frac{864}{3} \pi\) \(V=288 \pi\ \text{ft}^3\) Remember that you need to label your answer with the unit given in the problem statement. |
A sphere has a radius of 7 inches. What is the volume of the sphere? Round your final answer to the nearest hundredth.
\(V \approx 457.33 \pi\ \text{in}^3\)
If you need help arriving at this answer, click the Solution button.
Step 1: Substitute the radius into the volume equation. |
\(V=\frac{4}{3} \pi r^3\) \(V=\frac{4}{3} \pi^(7)3\) |
Step 2: Cube the radius. |
\(V=\frac{4}{3} \pi(7)(7)(7)\) \(V=\frac{4}{3} \pi(343)\) |
Step 3: Simplify. Round your final answer to the nearest hundredth. Leave pi as the symbol \(\pi\). |
\( V = \frac{1,372}{3} \pi\) \(V \approx 457.33 \pi\ \text{in}^3\) Remember that you need to label your answer with the unit given in the problem statement. |
