To solve the literal equation $SA = 4 \pi r^2$ for $r$, follow these steps:

Step 1: Start with the given equation.

$SA = 4 \pi r^2$ Where:

• $SA$ is the surface area,
• $r$ is the radius,
• $\pi$ is a constant (approximately 3.14159).

Step 2: Isolate $r^2$.

To solve for $r$, we need to isolate $r^2$. Start by dividing both sides of the equation by $4 \pi$: $\frac{SA}{4 \pi} = r^2$

Step 3: Take the square root of both sides.

Now, to solve for $r$, take the square root of both sides: $r = \sqrt{\frac{SA}{4 \pi}}$

This is the solution for $r$ in terms of the surface area $SA$.

Final Answer:

$r = \sqrt{\frac{SA}{4 \pi}}$

Would you like to go over any details or have questions?

Here are 5 related questions you might consider:

1. How do you apply this formula to calculate the radius when a specific surface area is given?
2. What are the units for the surface area $SA$ and how do they relate to the units of $r$?
3. How does this formula change if you are solving for $SA$ instead?
4. How does the value of $\pi$ affect the result in practical calculations?
5. What happens to $r$ if you double the surface area $SA$?

Tip: When working with literal equations, always aim to isolate the variable of interest by using inverse operations systematically.