Answer :
To determine the length of the diameter of a circle given its area, we can follow a series of steps:
1. Identify the formula for the area of a circle: The formula to calculate the area of a circle is [tex]\( A = \pi r^2 \)[/tex], where [tex]\( A \)[/tex] is the area, [tex]\(\pi\)[/tex] (pi) is approximately 3.14, and [tex]\( r \)[/tex] is the radius of the circle.
2. Isolate the radius in the area formula:
[tex]\[ r^2 = \frac{A}{\pi} \][/tex]
Therefore, to find the radius [tex]\( r \)[/tex], we rearrange the formula to:
[tex]\[ r = \sqrt{\frac{A}{\pi}} \][/tex]
3. Substitute the given area into the formula:
Given:
[tex]\[ A = 379.94 \, \text{cm}^2 \][/tex]
Substitute [tex]\( A \)[/tex] and [tex]\(\pi\)[/tex]:
[tex]\[ r = \sqrt{\frac{379.94}{3.14}} \][/tex]
4. Calculate the radius:
[tex]\[ r = \sqrt{121} \][/tex]
This simplifies to:
[tex]\[ r = 11.0 \, \text{cm} \][/tex]
5. Find the diameter:
The diameter [tex]\( d \)[/tex] of a circle is twice the radius:
[tex]\[ d = 2r \][/tex]
6. Substitute the radius to get the diameter:
Since [tex]\( r = 11.0 \, \text{cm} \)[/tex]:
[tex]\[ d = 2 \times 11.0 \, \text{cm} = 22.0 \, \text{cm} \][/tex]
Thus, the length of the diameter of the circle is [tex]\( 22.0 \, \text{cm} \)[/tex].
Given the options:
A. 11.0 cm
B. 121.0 cm
Neither option directly matches the diameter we computed. However, if the question intended to check understanding of the radius as hinted by option A, 11.0 cm could be regarded as the radius rather than the diameter. The correct interpretation from the problem-solving steps is that:
- The radius is 11.0 cm.
- The diameter is 22.0 cm.
Neither provided option corresponds to the correct diameter directly, but for clarity, option A might refer to the radius.
1. Identify the formula for the area of a circle: The formula to calculate the area of a circle is [tex]\( A = \pi r^2 \)[/tex], where [tex]\( A \)[/tex] is the area, [tex]\(\pi\)[/tex] (pi) is approximately 3.14, and [tex]\( r \)[/tex] is the radius of the circle.
2. Isolate the radius in the area formula:
[tex]\[ r^2 = \frac{A}{\pi} \][/tex]
Therefore, to find the radius [tex]\( r \)[/tex], we rearrange the formula to:
[tex]\[ r = \sqrt{\frac{A}{\pi}} \][/tex]
3. Substitute the given area into the formula:
Given:
[tex]\[ A = 379.94 \, \text{cm}^2 \][/tex]
Substitute [tex]\( A \)[/tex] and [tex]\(\pi\)[/tex]:
[tex]\[ r = \sqrt{\frac{379.94}{3.14}} \][/tex]
4. Calculate the radius:
[tex]\[ r = \sqrt{121} \][/tex]
This simplifies to:
[tex]\[ r = 11.0 \, \text{cm} \][/tex]
5. Find the diameter:
The diameter [tex]\( d \)[/tex] of a circle is twice the radius:
[tex]\[ d = 2r \][/tex]
6. Substitute the radius to get the diameter:
Since [tex]\( r = 11.0 \, \text{cm} \)[/tex]:
[tex]\[ d = 2 \times 11.0 \, \text{cm} = 22.0 \, \text{cm} \][/tex]
Thus, the length of the diameter of the circle is [tex]\( 22.0 \, \text{cm} \)[/tex].
Given the options:
A. 11.0 cm
B. 121.0 cm
Neither option directly matches the diameter we computed. However, if the question intended to check understanding of the radius as hinted by option A, 11.0 cm could be regarded as the radius rather than the diameter. The correct interpretation from the problem-solving steps is that:
- The radius is 11.0 cm.
- The diameter is 22.0 cm.
Neither provided option corresponds to the correct diameter directly, but for clarity, option A might refer to the radius.
