Respuesta :
Answer:
[tex]4\sqrt{15} \ cm[/tex]
Step-by-step explanation:
Steps:
- First, we need to find out what is the fraction of circle from the area 12 cm².
- Then we can find the total area of the circle.
- Then we can find the radius of the circle.
Total angle of a circle = 2π rad. Therefore the fraction of 1/10 rad:
[tex]\boxed{circle's\ angle : circle's\ area = fraction's\ angle : fraction's\ area}[/tex]
[tex]2\pi : circle's\ area=\frac{1}{10} :12[/tex]
[tex]circle's\ area=2\pi\times12\div\frac{1}{10}[/tex]
[tex]=240\pi\ cm^2[/tex]
Area of a circle = πr²
[tex]240\pi=\pi r^2[/tex]
[tex]240=r^2[/tex]
[tex]r=\sqrt{240}[/tex]
[tex]r=4\sqrt{15} \ cm[/tex]
Final answer:
To find the radius of a circle with a sector area of 12 square centimeters and a central angle of ⅒ radian, use the formula r = √(2A/θ), where r is the radius, A is the area, and θ is the central angle. Substituting the given values, the radius is approximately 15.49 cm.
Explanation:
To find the radius of a circle that has a sector of area 12 square centimeters determined by a central angle of ⅒ radian, we can use the formula for the area of a sector: A = (θ/2) * r^2, where θ is the central angle and r is the radius of the circle. Rearranging the formula, we have r = √(2A/θ). Substituting the given values, we have r = √(2 * 12 / ⅒) = √(24 / ⅒) = √(240).
Since the question asks for the radius in centimeters, it is important to note that the units of our intermediate calculations were in square centimeters. Therefore, the radius will also be in centimeters. Taking the square root of 240, we find that the radius is approximately 15.49 cm.
