Question

the radius of a circle is 10 meters. what is the angle measure of an arc bounding a sector with area 4π square meters? k = 4π sq. m r = 10 m give the exact answer in simplest form.

Explanation:

Step1: Sector area formula

$A = \frac{\theta}{360^\circ} \cdot \pi r^2$

Step2: Substitute known values

$4\pi = \frac{\theta}{360^\circ} \cdot \pi (10)^2$

Step3: Simplify radius squared

$4\pi = \frac{\theta}{360^\circ} \cdot 100\pi$

Step4: Cancel π and solve for θ

$4 = \frac{100\theta}{360^\circ} \implies \theta = \frac{4 \cdot 360^\circ}{100} = \frac{1440^\circ}{100} = \frac{72^\circ}{5}$

Answer:

$\frac{72}{5}^\circ$