The area of a sector of a circle with a central angle of 120° is
70 m2.
Find the radius of the circle. (Round your answer to one decimal place.)

To find the radius of the circle given the area of a sector and the central angle, we can use the formula for the area of a sector:

\[
A = \frac{\theta}{360^\circ} \times \pi r^2
\]

Where:
- \( A \) is the area of the sector.
- \( \theta \) is the central angle in degrees.
- \( r \) is the radius of the circle.

Given:
- \( A = 70 \, \text{m}^2 \)
- \( \theta = 120^\circ \)

We need to solve for \( r \). Plugging in the given values:

\[
70 = \frac{120^\circ}{360^\circ} \times \pi r^2
\]

Simplify the fraction:

\[
70 = \frac{1}{3} \times \pi r^2
\]

Multiply both sides by 3 to solve for \( \pi r^2 \):

\[
210 = \pi r^2
\]

Now, divide both sides by \( \pi \) to solve for \( r^2 \):

\[
r^2 = \frac{210}{\pi}
\]

Finally, take the square root of both sides to find \( r \):

\[
r = \sqrt{\frac{210}{\pi}}
\]

Let's calculate the value of \( r \) to one decimal place.The radius of the circle is approximately \( 8.2 \) meters.

Do you want more details or have any questions?

Here are some related questions for further exploration:

1. How would the radius change if the central angle were \( 90^\circ \)?
2. What is the formula for the circumference of the entire circle?
3. How do you calculate the length of the arc corresponding to the sector?
4. How would the area change if the radius were doubled?
5. Can you derive the formula for the area of a sector from the formula for the area of a circle?

**Tip:** When dealing with sectors, always ensure the angle is in degrees unless specified otherwise, as this affects how you apply the formulas.

Learn how to find the radius of a circle sector with a 120° central angle and an area of 70 m². Step-by-step solution using the area of a sector formula. Suitable for high school students.

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