How do you find the radius with the area of a sector of a circle with a sector which its area is 12pi cm^2 and the angle is 120°?

Question

Eva Abramson · Accepted Answer

The radius is 6 cm.

A full circle has 360°, so 120° is 1/3 of the circle. We can use this to find the full area of the circle from which the sector was cut: #(120°)/(360°)=(12pi)/x \rightarrowx=36pi# Since the full area of the circle is #36pi# and the area of a circle is #A=pi*r^2#, we know that: #pi*r^2=36pi# #r^2=36# #r=6# We ignore the negative value since the radius should be positive. Since the units of the area are cm^2, the units for the radius are just cm.

Abigail Allen · Answer

undefined To find the radius $ r $ of a sector of a circle with an area of $ 12\pi \, \text{cm}^2 $ and an angle of $ 120^\circ $, you can use the formula:

$$ \text{Area of sector} = \frac{\text{angle}}{360^\circ} \times \pi r^2 $$

Rearranging the formula to solve for $ r $:

$$ r = \sqrt{\frac{\text{Area of sector} \times 360^\circ}{\text{angle} \times \pi}} $$

Substituting the given values:

$$ r = \sqrt{\frac{12\pi \times 360^\circ}{120^\circ \times \pi}} $$

$$ r = \sqrt{\frac{4320}{120}} $$

$$ r = \sqrt{36} $$

$$ r = 6 \, \text{cm} $$