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Answer :
To find the length of the radius of a circle when the area is given, we can use the formula for the area of a circle:
[tex]\[ \text{Area} = \pi \times r^2 \][/tex]
where [tex]\(\text{Area}\)[/tex] is the area of the circle and [tex]\(r\)[/tex] is the radius.
Given:
- The area of the circle is [tex]\(38.5 \, \text{cm}^2\)[/tex].
- We are using an approximate value for [tex]\(\pi\)[/tex] as [tex]\(\frac{22}{7}\)[/tex].
Let's find the radius step-by-step:
1. Set up the equation:
[tex]\[ 38.5 = \frac{22}{7} \times r^2 \][/tex]
2. Solve for [tex]\(r^2\)[/tex]:
To isolate [tex]\(r^2\)[/tex], multiply both sides by [tex]\(\frac{7}{22}\)[/tex]:
[tex]\[ r^2 = 38.5 \times \frac{7}{22} \][/tex]
3. Calculate [tex]\(r^2\)[/tex]:
[tex]\[ r^2 = \frac{38.5 \times 7}{22} \][/tex]
4. Find the value of [tex]\(r\)[/tex]:
Take the square root of both sides to find [tex]\(r\)[/tex]:
[tex]\[ r = \sqrt{\frac{38.5 \times 7}{22}} \][/tex]
5. Calculate the radius [tex]\(r\)[/tex]:
After calculating, you find that:
[tex]\[ r = 3.5 \, \text{cm} \][/tex]
So, the length of the radius of the circle is [tex]\(3.5 \, \text{cm}\)[/tex].
[tex]\[ \text{Area} = \pi \times r^2 \][/tex]
where [tex]\(\text{Area}\)[/tex] is the area of the circle and [tex]\(r\)[/tex] is the radius.
Given:
- The area of the circle is [tex]\(38.5 \, \text{cm}^2\)[/tex].
- We are using an approximate value for [tex]\(\pi\)[/tex] as [tex]\(\frac{22}{7}\)[/tex].
Let's find the radius step-by-step:
1. Set up the equation:
[tex]\[ 38.5 = \frac{22}{7} \times r^2 \][/tex]
2. Solve for [tex]\(r^2\)[/tex]:
To isolate [tex]\(r^2\)[/tex], multiply both sides by [tex]\(\frac{7}{22}\)[/tex]:
[tex]\[ r^2 = 38.5 \times \frac{7}{22} \][/tex]
3. Calculate [tex]\(r^2\)[/tex]:
[tex]\[ r^2 = \frac{38.5 \times 7}{22} \][/tex]
4. Find the value of [tex]\(r\)[/tex]:
Take the square root of both sides to find [tex]\(r\)[/tex]:
[tex]\[ r = \sqrt{\frac{38.5 \times 7}{22}} \][/tex]
5. Calculate the radius [tex]\(r\)[/tex]:
After calculating, you find that:
[tex]\[ r = 3.5 \, \text{cm} \][/tex]
So, the length of the radius of the circle is [tex]\(3.5 \, \text{cm}\)[/tex].
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