Question
The circumference of a circle is 351321 in.
What is the approximate diameter of the circle?
Use 227 for Ο.
Enter your answer as a mixed number in simplest form in the box.
in.
What is the approximate diameter of the circle?
Use 227 for Ο.
Enter your answer as a mixed number in simplest form in the box.
in.
Answers
GPT-4o mini
To find the diameter of the circle, we can use the formula for the circumference:
\[
C = \pi \times d
\]
where \(C\) is the circumference and \(d\) is the diameter. We can rearrange the formula to solve for \(d\):
\[
d = \frac{C}{\pi}
\]
Given that the circumference \(C\) is 351321 in and we are using \(\pi \approx \frac{22}{7}\), we can proceed with the calculation:
First, we will convert \(\pi\) into the fraction form for calculation, using \(\pi \approx \frac{22}{7}\):
\[
d = \frac{351321}{\frac{22}{7}} = 351321 \times \frac{7}{22}
\]
Calculating this gives:
\[
d = \frac{351321 \times 7}{22}
\]
Now, we can calculate \(351321 \times 7\):
\[
351321 \times 7 = 2459247
\]
Now, we divide this result by 22:
\[
d = \frac{2459247}{22}
\]
To perform the division:
1. Calculate \(2459247 \div 22\):
\[
2459247 \div 22 \approx 111350.31818 \ldots
\]
2. Now, we can express \(111350.31818\) as a mixed number. The whole part is 111350, and we take the decimal part, which is approximately \(0.31818\).
3. Convert \(0.31818\) into a fraction:
\[
0.31818 \approx \frac{31818}{100000} \approx \frac{15909}{50000} \text{ (approximating each decimal place)}
\]
The fraction of \(0.31818\) itself isnβt precise, but to keep things simple, recognizing \(0.31818\) as close to \(\frac{7}{22}\) may work well given itβs recurring.
As we finalize:
Thus, the diameter of the circle is approximately:
\[
\text{Diameter} \approx 111350 \frac{7}{22}
\]
Putting this together, the diameter of the circle, as a mixed number in simplest form, is:
\[
\boxed{111350 \frac{7}{22}} \text{ in.}
\]
\[
C = \pi \times d
\]
where \(C\) is the circumference and \(d\) is the diameter. We can rearrange the formula to solve for \(d\):
\[
d = \frac{C}{\pi}
\]
Given that the circumference \(C\) is 351321 in and we are using \(\pi \approx \frac{22}{7}\), we can proceed with the calculation:
First, we will convert \(\pi\) into the fraction form for calculation, using \(\pi \approx \frac{22}{7}\):
\[
d = \frac{351321}{\frac{22}{7}} = 351321 \times \frac{7}{22}
\]
Calculating this gives:
\[
d = \frac{351321 \times 7}{22}
\]
Now, we can calculate \(351321 \times 7\):
\[
351321 \times 7 = 2459247
\]
Now, we divide this result by 22:
\[
d = \frac{2459247}{22}
\]
To perform the division:
1. Calculate \(2459247 \div 22\):
\[
2459247 \div 22 \approx 111350.31818 \ldots
\]
2. Now, we can express \(111350.31818\) as a mixed number. The whole part is 111350, and we take the decimal part, which is approximately \(0.31818\).
3. Convert \(0.31818\) into a fraction:
\[
0.31818 \approx \frac{31818}{100000} \approx \frac{15909}{50000} \text{ (approximating each decimal place)}
\]
The fraction of \(0.31818\) itself isnβt precise, but to keep things simple, recognizing \(0.31818\) as close to \(\frac{7}{22}\) may work well given itβs recurring.
As we finalize:
Thus, the diameter of the circle is approximately:
\[
\text{Diameter} \approx 111350 \frac{7}{22}
\]
Putting this together, the diameter of the circle, as a mixed number in simplest form, is:
\[
\boxed{111350 \frac{7}{22}} \text{ in.}
\]