Question

What is the area of a circle with a diameter of 10 millimeters? Estimate the area to the tenths place using 3.14 for π
π
.(1 point)
Responses

79 square mm
79 square mm

78.5 square mm
78.5 square mm

314 square mm
314 square mm

15.7 square mm
15.7 square mm

Be sure to explain the steps first please

Answer 1

To find the area of a circle, we use the formula:

\[
\text{Area} = \pi r^2
\]

where \( r \) is the radius of the circle.

1. **Find the radius**: The radius is half of the diameter. Given that the diameter of the circle is 10 millimeters, we calculate the radius as follows:

\[
r = \frac{\text{diameter}}{2} = \frac{10 \text{ mm}}{2} = 5 \text{ mm}
\]

2. **Substitute the radius into the area formula**: Now that we have the radius, we can substitute it into the area formula:

\[
\text{Area} = \pi (5 \text{ mm})^2
\]

3. **Calculate \( 5^2 \)**:

\[
5^2 = 25
\]

4. **Use \(\pi \approx 3.14\)**: Now substitute the value of \(\pi\):

\[
\text{Area} \approx 3.14 \times 25
\]

5. **Calculate the area**: Multiply \( 3.14 \) by \( 25 \):

\[
3.14 \times 25 = 78.5 \text{ square mm}
\]

Thus, the estimated area of the circle to the tenths place is:

\[
\text{Area} \approx 78.5 \text{ square mm}
\]

Therefore, the correct response is:

**78.5 square mm**.