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Answer :
To solve the problem of finding the radius of a circle given its circumference is 66 cm, and using [tex]\(\pi = \frac{22}{7}\)[/tex], you can follow these steps:
1. Understand the Formula:
The circumference (perimeter) of a circle is calculated using the formula:
[tex]\[
\text{Circumference} = 2 \pi r
\][/tex]
where [tex]\( r \)[/tex] is the radius of the circle.
2. Substitute the Given Values:
You're given that the circumference of the circle is 66 cm and [tex]\(\pi\)[/tex] is approximated as [tex]\(\frac{22}{7}\)[/tex].
3. Set Up the Equation:
Plug the known values into the formula:
[tex]\[
66 = 2 \times \left(\frac{22}{7}\right) \times r
\][/tex]
4. Solve for the Radius [tex]\( r \)[/tex]:
- First, simplify the expression [tex]\(2 \times \frac{22}{7}\)[/tex]:
[tex]\[
2 \times \frac{22}{7} = \frac{44}{7}
\][/tex]
- Now, substitute back into the equation:
[tex]\[
66 = \frac{44}{7} \times r
\][/tex]
- Isolate [tex]\( r \)[/tex] by multiplying both sides by [tex]\(\frac{7}{44}\)[/tex]:
[tex]\[
r = 66 \times \frac{7}{44}
\][/tex]
- Simplify the multiplication:
- Divide 66 by 44, which simplifies as:
[tex]\[
\frac{66}{44} = \frac{3}{2}
\][/tex]
- Then multiply by 7:
[tex]\[
r = \frac{3}{2} \times 7 = \frac{21}{2} = 10.5
\][/tex]
5. Conclusion:
The radius of the circle is 10.5 cm.
Thus, the correct answer is [tex]\(d. 10.5 \text{ cm}\)[/tex].
1. Understand the Formula:
The circumference (perimeter) of a circle is calculated using the formula:
[tex]\[
\text{Circumference} = 2 \pi r
\][/tex]
where [tex]\( r \)[/tex] is the radius of the circle.
2. Substitute the Given Values:
You're given that the circumference of the circle is 66 cm and [tex]\(\pi\)[/tex] is approximated as [tex]\(\frac{22}{7}\)[/tex].
3. Set Up the Equation:
Plug the known values into the formula:
[tex]\[
66 = 2 \times \left(\frac{22}{7}\right) \times r
\][/tex]
4. Solve for the Radius [tex]\( r \)[/tex]:
- First, simplify the expression [tex]\(2 \times \frac{22}{7}\)[/tex]:
[tex]\[
2 \times \frac{22}{7} = \frac{44}{7}
\][/tex]
- Now, substitute back into the equation:
[tex]\[
66 = \frac{44}{7} \times r
\][/tex]
- Isolate [tex]\( r \)[/tex] by multiplying both sides by [tex]\(\frac{7}{44}\)[/tex]:
[tex]\[
r = 66 \times \frac{7}{44}
\][/tex]
- Simplify the multiplication:
- Divide 66 by 44, which simplifies as:
[tex]\[
\frac{66}{44} = \frac{3}{2}
\][/tex]
- Then multiply by 7:
[tex]\[
r = \frac{3}{2} \times 7 = \frac{21}{2} = 10.5
\][/tex]
5. Conclusion:
The radius of the circle is 10.5 cm.
Thus, the correct answer is [tex]\(d. 10.5 \text{ cm}\)[/tex].
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