Question
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Question
A button has a diameter of 0.80 𝑖𝑛𝑐ℎ𝑒𝑠.
What is the exact area of the button in terms of pi (𝜋)?
(1 point)
Responses
0.16𝜋 𝑖𝑛2
0.16𝜋 𝑖𝑛2
0.40𝜋 𝑖𝑛2
0.40𝜋 𝑖𝑛2
0.64𝜋 𝑖𝑛2
0.64𝜋 𝑖𝑛2
0.80𝜋 𝑖𝑛2
0.80𝜋 𝑖𝑛2
Answers
GPT-4o mini
To find the area \( A \) of a button with a diameter of 0.80 inches, we can use the formula for the area of a circle:
\[
A = \pi r^2
\]
where \( r \) is the radius. The radius is half of the diameter:
\[
r = \frac{0.80 \text{ inches}}{2} = 0.40 \text{ inches}
\]
Now we can substitute the radius into the area formula:
\[
A = \pi (0.40 \text{ inches})^2
\]
Calculating \( (0.40)^2 \):
\[
(0.40)^2 = 0.16
\]
Now, substitute this back into the area formula:
\[
A = \pi \times 0.16 \text{ in}^2 = 0.16\pi \text{ in}^2
\]
Therefore, the exact area of the button in terms of pi is:
**0.16𝜋 𝑖𝑛²**.
\[
A = \pi r^2
\]
where \( r \) is the radius. The radius is half of the diameter:
\[
r = \frac{0.80 \text{ inches}}{2} = 0.40 \text{ inches}
\]
Now we can substitute the radius into the area formula:
\[
A = \pi (0.40 \text{ inches})^2
\]
Calculating \( (0.40)^2 \):
\[
(0.40)^2 = 0.16
\]
Now, substitute this back into the area formula:
\[
A = \pi \times 0.16 \text{ in}^2 = 0.16\pi \text{ in}^2
\]
Therefore, the exact area of the button in terms of pi is:
**0.16𝜋 𝑖𝑛²**.