How to Calculate the Cubic Feet of a Circle

How to Calculate the Cubic Feet of a Circle
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If your teacher has asked you to find the cubic feet of a circle, it might be a trick question. "Cubic feet" or feet3 is a clue that you're working in three dimensions, which means you're actually looking for the volume of a three-dimensional circle, which is a sphere. A beach ball, a globe or a soap bubble are all familiar examples of spheres.

The formula for finding the volume of a sphere is:

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

where ​r​ is the radius of the sphere.

You'll Need to Know the Radius

In order to calculate the volume of a sphere in cubic feet, you'll need to know the radius of the sphere. The radius is the distance from the very center of the sphere to any point on the sphere's surface. If you're not given the radius directly, you might get the diameter or the circumference of the sphere.

The diameter is the distance all the way from any point on the sphere, through the center of the sphere, and then continuing in a straight line to the outside of the sphere. It's also exactly twice the radius of the sphere, so if you're given the diameter, simply divide by two to get the radius. So if your sphere has a diameter of 10 feet, your radius is:

\frac{10}{2}=5\text{ feet}

The circumference of the sphere is the measurement you'd get if you wrapped a measuring tape all the way around its outside. Imagine measuring the equator all the way around the globe. That's the circumference of a sphere. If you have the circumference, you can divide it by π to get the diameter, then divide the result by 2 to get the radius. So if a sphere's circumference is 56.52 feet, you'd calculate:

\text{diameter}=\frac{56.52\text{ feet}}{\pi}=18\text{ feet}\\\text{ }\\\text{radius}=\frac{18\text{ feet}}{2}=9\text{ feet}

Calculating the Volume of Your Sphere

Now that you have the radius of your sphere in feet, it's time to calculate its volume.

Warnings

  • Is your radius measured in feet? If not, you'll need to convert whatever unit of measure it does use to feet before you continue.

    Cube the radius or, to put it another way, multiply the radius by itself three times. So if the radius of your sphere is 4 feet, you'd have:

    (4\text{ feet})^3=4\text{ feet}\times 4\text{ feet}\times 4\text{ feet}=64\text{ feet}^3

    Multiply the result from Step 1 by 4/3. To continue the example, you'd have:

    \frac{4}{3}64\text{ feet}^3=85.33\text{ feet}^3

    Your teacher will tell you how many decimal places you should round to. Also, note that you continue carrying the unit of measure along with your calculations.

    Finish your calculation by multiplying the result from Step 2 by π. The result is the volume of your sphere in cubic feet. To conclude the example, it works out to:

    \pi \times 85.33\text{ feet}^3=267.94\text{ feet}^3

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