Let's Break it Down
Now that you know how to identify a sphere, it’s time to learn how to calculate its volume. The formula to find the volume of a sphere is shown.
Volume of a Sphere
The volume of a sphere with radius, r, is \(V=\frac{4}{3} \pi r^3\).
The radius, \(r\), is the distance from the center of the sphere to any point on the sphere’s surface. When calculating the volume of a sphere, \(r\) is cubed. What does it mean to cube \(r\)?
To cube \(r\) means to multiply the radius by itself three times.
As an example, if \(r=3\), then \(r^3=(3)(3)(3)=(9)(3)=27\)
You use the formula \(V=\frac{4}{3} \pi r^3\) to find the volume of a sphere. Click each tab to see an example. The number pi is included in the answers as the symbol \(\pi\).
A sphere has a radius of \(2\) cm. What is the volume of the sphere?
Step 1: Substitute the radius into the volume equation. |
\(V=\frac{4}{3} \pi r^3\) \(V=\frac{4}{3} \pi(2)^3\) |
Step 2: Cube the radius. |
\(V=\frac{4}{3} \pi(2)(2)(2)\) \(V=\frac{4}{3} \pi(8)\) |
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Step 3: Simplify. Round your answer to the nearest hundredth. Leave pi as the symbol \(\pi\). |
\(V=\frac{32}{3} \pi\) \(V \approx 10.67 \pi\ \text{cm}^3\) Remember that you need to label your answer with the unit given in the problem statement. |
A sphere has a radius of \(3\) inches. What is the volume of the sphere?
Step 1: Substitute the radius into the volume equation. |
\(V=\frac{4}{3} \pi r^3\) \(V=\frac{4}{3} \pi(3)^3\) |
Step 2: Cube the radius. |
\(V=\frac{4}{3} \pi(3)(3)(3)\) \(V=\frac{4}{3} \pi(27)\) |
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Step 3: Simplify. Leave pi as the symbol \(\pi\). |
\(V=\frac{108}{3} \pi\) \(V=36 \pi\ \text{in}^3\) Remember that you need to label your answer with the unit given in the problem statement. |
A sphere has a radius of 4 feet. What is the volume of the sphere?
Step 1: Substitute the radius into the volume equation. |
\(V=\frac{4}{3} \pi r^3\) \(V=\frac{4}{3} \pi(4)^3\) |
Step 2: Cube the radius. |
\(V=\frac{4}{3} \pi(4)(4)(4)\) \(V=\frac{4}{3} \pi(64)\) |
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Step 3: Simplify. Round your final answer to the nearest hundredth. Leave pi as the symbol \(\pi\). |
\(V=\frac{256}{3} \pi\) \(V \approx 85.33 \pi\ \text{ft}^3\) Remember that you need to label your answer with the unit given in the problem statement. |
