Question
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
Nice!
Next, let's use 3.14 as an approximation for π. Show that we can substitute 3.14 for π in the equation.
r
Input Output Arrow
πr
2
Input Output Arrow
A
A = πr
2
A = π (7)
2
A ≈
3.14
· (7)
2
Great job!
Now, use your equation to find the approximate circumference of a circle with a radius of 7. What's 3.14·7
2
?
r
Input Output Arrow
πr
2
Input Output Arrow
A
A = πr
2
A = π (7)
2
A ≈ 3.14 · (7)
2
A ≈
Answers
GPT-4o mini
To find the approximate area of a circle with a radius of 7 using the equation \( A = \pi r^2 \) and using 3.14 as an approximation for \( \pi \), we follow these steps:
1. Substitute \( r = 7 \) into the equation:
\[
A = \pi (7)^2
\]
2. Substitute 3.14 for \( \pi \):
\[
A \approx 3.14 \cdot (7)^2
\]
3. Calculate \( (7)^2 \):
\[
(7)^2 = 49
\]
4. Substitute that value back into the equation:
\[
A \approx 3.14 \cdot 49
\]
5. Finally, calculate \( 3.14 \cdot 49 \):
\[
A \approx 3.14 \cdot 49 = 153.86
\]
Thus, the approximate area of the circle with a radius of 7 is \( A \approx 153.86 \).
1. Substitute \( r = 7 \) into the equation:
\[
A = \pi (7)^2
\]
2. Substitute 3.14 for \( \pi \):
\[
A \approx 3.14 \cdot (7)^2
\]
3. Calculate \( (7)^2 \):
\[
(7)^2 = 49
\]
4. Substitute that value back into the equation:
\[
A \approx 3.14 \cdot 49
\]
5. Finally, calculate \( 3.14 \cdot 49 \):
\[
A \approx 3.14 \cdot 49 = 153.86
\]
Thus, the approximate area of the circle with a radius of 7 is \( A \approx 153.86 \).