Upper A equals one seventh pi r cubed left parenthesis b minus 8 right parenthesis
​; b

The expression you've provided can be interpreted as:

\[ A = \frac{1}{7} \pi r^3 (b - 8) \]

This equation involves several variables:
- \( A \): the quantity you're solving for.
- \( r \): the radius.
- \( b \): another variable.

If you're interested in solving for \( b \), we can rearrange the equation. Here's how you would do that:

1. Start with the given equation:
   \[
   A = \frac{1}{7} \pi r^3 (b - 8)
   \]

2. Multiply both sides by 7 to eliminate the fraction:
   \[
   7A = \pi r^3 (b - 8)
   \]

3. Divide both sides by \( \pi r^3 \) to isolate \( (b - 8) \):
   \[
   \frac{7A}{\pi r^3} = b - 8
   \]

4. Finally, add 8 to both sides to solve for \( b \):
   \[
   b = \frac{7A}{\pi r^3} + 8
   \]

So, the variable \( b \) is given by:

\[
b = \frac{7A}{\pi r^3} + 8
\]

Would you like further details, or do you have any questions? Here are some related questions you might find interesting:

1. How would you solve for \( r \) in the original equation?
2. What happens to \( b \) if \( A \) is doubled?
3. Can you find a relationship between \( A \) and \( r \) if \( b \) is constant?
4. What is the significance of the constant \( \pi \) in this equation?
5. How would you interpret this equation in a real-world context?

**Tip:** When manipulating equations, always perform the same operation on both sides to maintain equality.

Understand how to solve the equation A = (1/7)πr³(b - 8) for the variable b. Explore step-by-step solutions and mathematical concepts including equations, algebra, and geometry. Suitable for Grades 10-12.

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