Question

The area of a sector of a circle with a central angle of 5 radians is 15cm². Find the radius of the circle.

Do not round any intermediate computations. Round your answer to the nearest tenth.

Answer 1

The area of a sector of a circle is equal to the central angle in radians multiplied by the square of the radius.

Therefore, we can use this formula to solve for the radius:

Area = (Central Angle) × (Radius)²

Therefore, we can rearrange this formula to solve for the radius:

Radius = √(Area / Central Angle)

Plugging in the values given, we get:

Radius = √(15 cm² / 5 rad)

Simplifying, we get:

Radius = 3 cm

Therefore, the radius of the circle is 3 cm, rounded to the nearest tenth.