Question

If the circle has area 128cm² and radius 8 cm, what will its central angle be?

a) 22.5 degrees
b) 45 degrees
c) 90 degrees
d) 180 degrees

Answer 1

The central angle of the circle with an area of 128cm² and a radius of 8cm is approximately 90 degrees.

Step-by-step explanation:

The formula for the area of a circle is A = πr², where A is the area of the circle and r is the radius. In this case, the area of the circle is given as 128cm² and the radius is given as 8cm. We can solve for the central angle by using the formula for the area of a sector: A = (θ/360) × πr², where θ is the central angle.

Using the given values, we can set up the equation: 128 = (θ/360) × (π(8)²).

Simplifying the equation, we find: 128 = θ × 64 × π.

Dividing both sides of the equation by 64×π, we get: θ = 128/(64×π).

Calculating θ, we find: θ ≈ 90 degrees.