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Veronika [31]
3 years ago
13

An arc measures 50°in a circle with a radius of 8 cm. What is the area of the sector to the nearest tenth of a square centimeter

?
a.57.6m(squared)
b. 27.9m (squared)
c. 175m(squared)
d.7.0cm(squared)
Mathematics
1 answer:
marysya [2.9K]3 years ago
3 0

Answer:

27.9cm^2

Step-by-step explanation:

The <u>total area</u> of the circle is given by:

a=\pi r^2

where \pi is a constant \pi=3.1416

and r is the radius: r=8cm

Thus the total area of this circle is:

a=(3.1416)(8cm)^2\\a=(3.1416)(64cm^2)\\a=201.06cm^2

We want only the area of the arc that measures 50°. For this we must remember that the arc of the total circle is 360°.

Thus, we want 50° out of the 360° degrees in the circle. For this, we divide the total area by 360 and then we multiply by 50:

\frac{201.06cm^2}{360}(50)=0.5585cm^2(50)=27.9cm^2

the area of the sector to the nearest tenth is 27.9cm^2

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