Question

If we know r, the radius of a circle, we can find its area, A, using the rule πr
2
.
What are the independent and dependent variables in this situation?
r
Input Output Arrow
πr
2

Input Output Arrow
A
The independent variable is
r
.
The dependent variable is
A
.
You got it!
What equation represents this function? Write an equation in terms of π that shows how we can use the independent variable, r, to find the dependent variable, A.
r
Input Output Arrow
πr
2

Input Output Arrow
A
Nice!
Now, let’s find the output of this function when the input is 7. Start by substituting 7 for the radius, r.
r
Input Output Arrow
πr
2

Input Output Arrow
A
A = πr
2

A = π (
)
2

Answer 1

To find the area \( A \) of the circle when the radius \( r \) is 7, we can substitute 7 for \( r \) in the area formula \( A = \pi r^2 \).

Here’s how it looks step by step:

1. Start with the formula:
\[
A = \pi r^2
\]

2. Substitute \( r = 7 \):
\[
A = \pi (7)^2
\]

3. Calculate \( 7^2 \):
\[
7^2 = 49
\]

4. Now plug this back into the equation:
\[
A = \pi \cdot 49
\]

So, the area of the circle when the radius is 7 is:
\[
A = 49\pi
\]

This means the output of the function when the input is 7 is \( A = 49\pi \).