Question
If the circumference of a circle is 27 mm, then what is the diameter to the nearest tenth of a mm?
a. 84.8 mm
b. 8.6 mm
c. 4.3 mm
d. 17.2 mm
a. 84.8 mm
b. 8.6 mm
c. 4.3 mm
d. 17.2 mm
Answers
GPT-4o mini
To find the diameter of a circle when the circumference is given, we can use the formula for the circumference of a circle:
\[
C = \pi d
\]
where \( C \) is the circumference and \( d \) is the diameter. We can rearrange this formula to solve for \( d \):
\[
d = \frac{C}{\pi}
\]
Given that the circumference \( C = 27 \) mm, we can substitute this value into the formula:
\[
d = \frac{27}{\pi}
\]
Using the approximate value of \( \pi \approx 3.14\):
\[
d \approx \frac{27}{3.14} \approx 8.607 \text{ mm}
\]
Now, we need to round this to the nearest tenth of a mm:
\[
d \approx 8.6 \text{ mm}
\]
Thus, the diameter of the circle to the nearest tenth of a mm is:
**b. 8.6 mm**
\[
C = \pi d
\]
where \( C \) is the circumference and \( d \) is the diameter. We can rearrange this formula to solve for \( d \):
\[
d = \frac{C}{\pi}
\]
Given that the circumference \( C = 27 \) mm, we can substitute this value into the formula:
\[
d = \frac{27}{\pi}
\]
Using the approximate value of \( \pi \approx 3.14\):
\[
d \approx \frac{27}{3.14} \approx 8.607 \text{ mm}
\]
Now, we need to round this to the nearest tenth of a mm:
\[
d \approx 8.6 \text{ mm}
\]
Thus, the diameter of the circle to the nearest tenth of a mm is:
**b. 8.6 mm**