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Answer :
To find the value of the radius of the sector, let's follow these steps:
1. Understand the Problem:
We are given the area of a sector, which is [tex]\(38.5 \, \text{cm}^2\)[/tex], and we need to find the radius of the sector. The problem hints that [tex]\(\pi\)[/tex] should be approximated using [tex]\(\frac{22}{7}\)[/tex].
2. Use the Formula for the Area of a Sector:
The general formula for the area of a sector is:
[tex]\[
\text{Area of sector} = \left(\frac{\theta}{360}\right) \pi r^2
\][/tex]
where [tex]\(\theta\)[/tex] is the angle in degrees, [tex]\(\pi\)[/tex] is a constant (use [tex]\(\frac{22}{7}\)[/tex]), and [tex]\(r\)[/tex] is the radius.
3. Assumption Made:
Since no angle [tex]\(\theta\)[/tex] is provided, we'll assume it's a full circle ([tex]\(\theta = 360^\circ\)[/tex]). Therefore, the formula simplifies to the formula for the area of a circle:
[tex]\[
\pi r^2 = \text{Area of sector}
\][/tex]
4. Solve for the Radius:
[tex]\[
\pi r^2 = 38.5
\][/tex]
Substitute [tex]\(\pi = \frac{22}{7}\)[/tex]:
[tex]\[
\frac{22}{7} r^2 = 38.5
\][/tex]
5. Calculate [tex]\(r^2\)[/tex]:
[tex]\[
r^2 = \frac{38.5 \times 7}{22}
\][/tex]
[tex]\[
r^2 = 12.25
\][/tex]
6. Find [tex]\(r\)[/tex] (the radius):
To find the radius, take the square root of [tex]\(r^2\)[/tex]:
[tex]\[
r = \sqrt{12.25}
\][/tex]
[tex]\[
r = 3.5 \, \text{cm}
\][/tex]
Thus, the radius of the sector is [tex]\(3.5 \, \text{cm}\)[/tex].
1. Understand the Problem:
We are given the area of a sector, which is [tex]\(38.5 \, \text{cm}^2\)[/tex], and we need to find the radius of the sector. The problem hints that [tex]\(\pi\)[/tex] should be approximated using [tex]\(\frac{22}{7}\)[/tex].
2. Use the Formula for the Area of a Sector:
The general formula for the area of a sector is:
[tex]\[
\text{Area of sector} = \left(\frac{\theta}{360}\right) \pi r^2
\][/tex]
where [tex]\(\theta\)[/tex] is the angle in degrees, [tex]\(\pi\)[/tex] is a constant (use [tex]\(\frac{22}{7}\)[/tex]), and [tex]\(r\)[/tex] is the radius.
3. Assumption Made:
Since no angle [tex]\(\theta\)[/tex] is provided, we'll assume it's a full circle ([tex]\(\theta = 360^\circ\)[/tex]). Therefore, the formula simplifies to the formula for the area of a circle:
[tex]\[
\pi r^2 = \text{Area of sector}
\][/tex]
4. Solve for the Radius:
[tex]\[
\pi r^2 = 38.5
\][/tex]
Substitute [tex]\(\pi = \frac{22}{7}\)[/tex]:
[tex]\[
\frac{22}{7} r^2 = 38.5
\][/tex]
5. Calculate [tex]\(r^2\)[/tex]:
[tex]\[
r^2 = \frac{38.5 \times 7}{22}
\][/tex]
[tex]\[
r^2 = 12.25
\][/tex]
6. Find [tex]\(r\)[/tex] (the radius):
To find the radius, take the square root of [tex]\(r^2\)[/tex]:
[tex]\[
r = \sqrt{12.25}
\][/tex]
[tex]\[
r = 3.5 \, \text{cm}
\][/tex]
Thus, the radius of the sector is [tex]\(3.5 \, \text{cm}\)[/tex].
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