Given the formula for determining the volume of a sphere is 
V=4/3πr^3
Write the equation that you would solve to determine the radius of a sphere that has a volume of 88 cubic inches.

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

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

Given that the volume of the sphere is 88 cubic inches, substitute \( V = 88 \) into the formula:

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

Now, to solve for the radius \( r \), follow these steps:

1. Multiply both sides of the equation by \( \frac{3}{4} \) to isolate \( \pi r^3 \) on the right-hand side:

\[
\frac{3}{4} \times 88 = \pi r^3
\]

This simplifies to:

\[
66 = \pi r^3
\]

2. Divide both sides by \( \pi \):

\[
r^3 = \frac{66}{\pi}
\]

3. Take the cube root of both sides to find \( r \):

\[
r = \sqrt[3]{\frac{66}{\pi}}
\]

This is the equation you would solve to determine the radius of the sphere.

Would you like help solving this equation or any further details?

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Here are 5 related questions to expand on this concept:

1. How do you calculate the volume of a sphere if the radius is known?
2. How does the volume of a sphere change if the radius is doubled?
3. Can the formula for the surface area of a sphere be derived from its volume?
4. How is the formula for the volume of a sphere derived from calculus?
5. What is the relationship between the volume and surface area of a sphere?

**Tip**: To approximate the radius, you can use \( \pi \approx 3.1416 \).

Given the formula for determining the volume of a sphere is V = (4/3)πr^3, write the equation that you would solve to determine the radius of a sphere that has a volume of 88 cubic inches.

Learn how to find the radius of a sphere with a volume of 88 cubic inches using the formula V = (4/3)πr^3. This step-by-step guide breaks down the algebra and geometry concepts involved in solving for the radius, making it easy for high school students (Grades 9-12) to follow.

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