904.78 [tex]yards^{3}[/tex]
Step-by-step explanation:
The shape above is a sphere, the 3-D version of a circle.
Formula
The formula for the volume of a sphere is [tex]V=\frac{4}{3}\pi r^{3}[/tex], where V is the volume and r is the radius. Remember when using pi to use the pi button on the calculator to be precise.
Radius
The image above gives us the diameter. It shows the distance across the entire sphere is 12 yards. However, we need the diameter. Radius is equal to half of the diameter. So, the radius equals 6 yards.
Solving for V
Now that we have the information we need, we can plug in the values and solve.
First, rewrite the equation.
- [tex]V=\frac{4}{3}\pi 6^{3}[/tex]
Next, apply the exponents.
- [tex]V=\frac{4}{3}\pi *216[/tex]
Then, multiply out the terms.
- [tex]V=904.78[/tex]
This means that the volume of the sphere is 904.78 yards cubed.