To solve the problem of finding the diameter of a circle given its area, we need to follow a few steps:
1. Understand the given information:
- The area of the circle is given as [tex]\( 36 \pi \, \text{cm}^2 \)[/tex].
2. Recall the formula for the area of a circle:
- The formula for the area [tex]\( A \)[/tex] of a circle is [tex]\( A = \pi r^2 \)[/tex], where [tex]\( r \)[/tex] is the radius.
3. Set up the equation:
- Given [tex]\( A = 36 \pi \, \text{cm}^2 \)[/tex], we can set up the equation:
[tex]\[ 36 \pi = \pi r^2 \][/tex]
4. Solve for the radius [tex]\( r \)[/tex]:
- To isolate [tex]\( r^2 \)[/tex], divide both sides of the equation by [tex]\( \pi \)[/tex]:
[tex]\[ 36 = r^2 \][/tex]
- To find [tex]\( r \)[/tex], take the square root of both sides:
[tex]\[ r = \sqrt{36} \][/tex]
[tex]\[ r = 6 \, \text{cm} \][/tex]
5. Calculate the diameter:
- The diameter [tex]\( d \)[/tex] of a circle is twice the radius: [tex]\( d = 2r \)[/tex].
- So, [tex]\( d = 2 \times 6 \, \text{cm} \)[/tex].
6. Get the result:
- [tex]\( d = 12 \, \text{cm} \)[/tex]
Therefore, the diameter of the circle is [tex]\( 12 \, \text{cm} \)[/tex].
From the choices provided:
a. 6 cm
b. [tex]\( 1296 \pi \)[/tex] cm
c. 12 cm
d. [tex]\( 12 \pi \)[/tex] cm
The correct answer is:
C. 12 cm
