Question

The diameter of a circle is 10m. What is the angle measure of an arc bounding a sector area 5pi square meters?

Answer 1

Answer:

Angle measure of an arc is  72 °.

Step-by-step explanation:

Given : The diameter of a circle is 10m and sector area 5pi square meters.

To find :  What is the angle measure of an arc .

Solution : We have given that Diameter = 10 cm .

Radius =  $\frac{10}{2}$ =  5 cm.

Area of sector =  $\frac{theta}{360} *pi (r^{2} )$.

Plugging the values of r = 5cm  , Area of sector = 5 pi.

5 pi =  $\frac{theta}{360} *pi (5^{2} )$.

5 pi =  $\frac{theta}{360} *pi (25 )$.

On dividing by 25 pi

$\frac{5\ pi}{25\ pi}$ =  $\frac{theta}{360})$.

$\frac{1}{5}$ =  $\frac{theta}{360})$.

On multiplying both sides by 360 and swtiching sides.

Theta = $\frac{360}{5}$.

Theta = 72 °

Therefore, angle measure of an arc is  72 °.

Answer 2

 The area of the complete circle is:
 $A = pi * r ^ 2$
 Where,
 r: radius of the circle.
 Substituting values we have:
 $A = \pi * (10/2) ^ 2 A = \pi * (5) ^ 2 A = 25 \pi$
 Then, the measure of the angle of the arc whose area is 5pi is given by:
 $theta = A '/ A * (360)$
 Where,
 A '/ A: ratio of areas
 Substituting values:
 $theta = (5 \pi / 25 \pi ) * (360) theta = (5/25) * (360) theta = (1/5) * (360) theta = 72 degrees$
 Answer:
 the angle measure of an arc bounding to sector area 5pi square meters is:
 theta = 72 degrees