Solve each literal equations, involving square roots, for the requested variable. SA= 4 pied r squared

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.

Solve each literal equation, involving square roots, for the requested variable. SA = 4πr²

Discover how to solve the literal equation SA = 4πr² for the radius (r) in this step-by-step guide. Learn how to isolate the variable and apply square root operations. Ideal for students in Grades 9-12, covering key concepts in algebra and geometry.

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