To find the radius \( r \) of a circle given its circumference \( C \), we use the formula for the circumference:
\[ C = 2\pi r \]
Given that the circumference is \( 60\pi \), we can set up the equation:
\[ 60\pi = 2\pi r \]
Now, we can solve for \( r \):
- Divide both sides by \( 2\pi \):
\[ r = \frac{60\pi}{2\pi} \]
- Simplify:
\[ r = \frac{60}{2} = 30 \]
So, \( r = 30 \).
Now, let's look at the options you provided to see if we can express this correctly:
The correct way to express \( r \) that matches our result is to find the value based on the equation we derived. None of the provided responses is directly the answer \( r = 30 \), but to match with your choices:
The formulation \( r = \frac{60\pi}{2\pi} \) is equivalent to:
- Simplifying yields \( r = 30 \), but it doesn't appear on your options correctly.
From your options,:
- \( r= \frac{60\pi}{2\pi} \) essentially simplifies to \( r = 30 \).
So, the correct approach based on the answers you provided would be found through:
The closest and correct option that we derived is \( r = \frac{60\pi}{2\pi} \), which simplifies correctly to 30.
None of the other expressions you provided reflect the correct value of the radius, but this method shows the correct approach to find \( r \).
1 answer