Question

Circle N is shown. Line segment M L is a diameter. The length of N L is 6. Everything above angle M N L is shaded. The measure of central angle MNL is π radians, and the measure of the entire circle is 2π radians. The ratio of the measure of the central angle to the entire circle measure is . The area of the entire circle is π units2. The area of the sector is π units2.

Answer 1

Answer:

The ratio of the measure of the central angle to the entire circle measure$=\dfrac{1}{2}$

The area of the entire circle$=36\pi units^2.$

The area of the sector $=18\pi units^2$

Step-by-step explanation:

MNL is a diameter of the circle N

Radius, NL =6

• The measure of central angle MNL = π radians
• The measure of the entire circle = 2π radians.

The ratio of the measure of the central angle to the entire circle measure

$=\dfrac{\pi}{2\pi}\\\\ =\dfrac{1}{2}$

Area of a circle $=\pi r^2$

The area of the entire circle

$= \pi \times 6^2 \\=36\pi units^2.$

Therefore, the area of the sector

$=\dfrac{1}{2} \times 36\pi\\=18\pi units^2$