Question

If the area of a sector is 15π square centimeters and the radius of the circle is 5 centimeters,
find the measure of the central angle.

Answer 1

Answer:

∅ = 1.2π radians

Step-by-step explanation:

Area = 15π

Formula for area of sector = 0.5*∅*r², where ∅ is the sector's central angle

⇒ 15π = 0.5*∅*r²

⇒ 30π = r²*∅

Substituting r for 5,

30π = 25*∅

∴ ∅ = 1.2π radians

Answer 2

The measure of central angle is 216°

Step-by-step explanation:

Given : The area of a sector is = 15 π cm²

            Radius of the circle = 5 cm

To find: The measure of central angle

As we know area of a sector is given by

$area = \pi r^2 \dfrac{\theta }{360}$

where r is the radius and $\theta$ is the central angle of a circle

Now as according to question we have

$15\pi = \pi (5)^2\dfrac{\theta}{360} \\\\\Rightarrow 15 = 5\times 5\times \dfrac{\theta}{360}\\\\\Rightarrow \theta = \dfrac{15\times 360}{5\times 5 } = 216$

Hence,the measure of central angle is 216°

#Learn more

Find the area of a sector of a circle where central angle is 30° and the radius of the circle is 42 cm.​

brainly.in/question/13221252