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

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

Respuesta :

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

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 =  [tex]\frac{10}{2}[/tex] =  5 cm.

Area of sector =  [tex]\frac{theta}{360} *pi (r^{2} )[/tex].

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

5 pi =  [tex]\frac{theta}{360} *pi (5^{2} )[/tex].

5 pi =  [tex]\frac{theta}{360} *pi (25 )[/tex].

On dividing by 25 pi

[tex]\frac{5\ pi}{25\ pi}[/tex] =  [tex]\frac{theta}{360})[/tex].

[tex]\frac{1}{5}[/tex] =  [tex]\frac{theta}{360})[/tex].

On multiplying both sides by 360 and swtiching sides.

Theta = [tex]\frac{360}{5}[/tex].

Theta = 72 °

Therefore, angle measure of an arc is  72 °.

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