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nekit [7.7K]
3 years ago
14

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

Mathematics
2 answers:
olasank [31]3 years ago
8 0

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 °.

yulyashka [42]3 years ago
5 0
<span> The area of the complete circle is:
</span> A = pi * r ^ 2&#10;
<span> Where,
 r: radius of the circle.
 Substituting values we have:
</span> A =  \pi  * (10/2) ^ 2&#10;&#10;A =  \pi  * (5) ^ 2&#10;&#10;A = 25 \pi<span>
 Then, the measure of the angle of the arc whose area is 5pi is given by:
</span> theta = A '/ A * (360)&#10;
<span> Where,
 A '/ A: ratio of areas
 Substituting values:
</span> theta = (5 \pi  / 25 \pi ) * (360)&#10;&#10;theta = (5/25) * (360)&#10;&#10;theta = (1/5) * (360)  theta = 72 degrees<span>
 Answer:
 the angle measure of an arc bounding to sector area 5pi square meters is:
 theta = 72 degrees</span>
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