the volume of a sphere is 36pie ft3. what is the radius is the sphere

The volume \( V \) of a sphere is given by the formula:

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

Where:
- \( V \) is the volume of the sphere.
- \( r \) is the radius.
- \( \pi \) is Pi, approximately 3.14159.

You're given that the volume of the sphere is \( 36\pi \, \text{ft}^3 \), so we can set up the equation:

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

Now, divide both sides by \( \pi \) to simplify:

\[
36 = \frac{4}{3} r^3
\]

Next, multiply both sides by 3 to eliminate the fraction:

\[
108 = 4r^3
\]

Now, divide both sides by 4:

\[
r^3 = 27
\]

Finally, take the cube root of both sides to find \( r \):

\[
r = \sqrt[3]{27} = 3
\]

So, the radius of the sphere is \( r = 3 \, \text{ft} \).

Would you like more details or have any questions? Here are some related questions to expand your understanding:

1. What is the formula for the surface area of a sphere?
2. How does the volume of a sphere change if its radius is doubled?
3. What is the relationship between the volume of a sphere and a cube with the same radius?
4. Can you derive the volume formula of a sphere using calculus?
5. What is the difference in volume between two spheres with radii 3 ft and 6 ft?

**Tip**: When dealing with volume formulas, always make sure to work with consistent units for accurate calculations!

The volume of a sphere is 36π ft³. What is the radius of the sphere?

Learn how to find the radius of a sphere when its volume is given as 36π ft³. This problem involves key geometry concepts, including the formula for the volume of a sphere and solving for the radius. Suitable for students in Grades 8-10.

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