Question
What is the area of a circle with a diameter of 16 yards? Estimate the area to the hundredths place using 3.14 for π .
Answers
GPT-4o mini
To find the area of a circle with a given diameter, we can use the formula for the area of a circle:
\[
A = \pi r^2
\]
where \( r \) is the radius of the circle. The radius is half of the diameter. Given that the diameter is 16 yards, the radius is:
\[
r = \frac{16}{2} = 8 \text{ yards}
\]
Now, we can substitute the radius into the area formula using \( \pi \approx 3.14 \):
\[
A = 3.14 \times (8)^2
\]
Calculating \( (8)^2 \):
\[
(8)^2 = 64
\]
Now substitute this back into the area formula:
\[
A = 3.14 \times 64
\]
To calculate \( 3.14 \times 64 \):
\[
A = 200.96
\]
Thus, the area of the circle, estimated to the hundredths place, is:
\[
\boxed{200.96} \text{ square yards}
\]
\[
A = \pi r^2
\]
where \( r \) is the radius of the circle. The radius is half of the diameter. Given that the diameter is 16 yards, the radius is:
\[
r = \frac{16}{2} = 8 \text{ yards}
\]
Now, we can substitute the radius into the area formula using \( \pi \approx 3.14 \):
\[
A = 3.14 \times (8)^2
\]
Calculating \( (8)^2 \):
\[
(8)^2 = 64
\]
Now substitute this back into the area formula:
\[
A = 3.14 \times 64
\]
To calculate \( 3.14 \times 64 \):
\[
A = 200.96
\]
Thus, the area of the circle, estimated to the hundredths place, is:
\[
\boxed{200.96} \text{ square yards}
\]