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Find the area of a sector with a central angle of 133 degrees and a radius of 13.9 millimeters. Round to the nearest tenth.

A. 224.2 mm^2
B. 448.5 mm^2
C. 64.5 mm^2
D. 16.1 mm^2

Respuesta :

tyjmonet
The answer is A.
First, you change the degrees to radians.

133(pi/180)= 2.3212879051524583373085087220899 (long number)

Then you just plug that into the formula!

(r^2*theta)/2

(13.9^2 * 2.3212879051524583373085087220899) / 2 = 224.24801807725323767568848509749

Answer:

Area of sector = 224.2 mm².

Step-by-step explanation:

Given : a central angle of 133 degrees and a radius of 13.9 millimeters.

To find : Find the area of a sector.

Solution : We have given that

central angle =  133 degrees

Radius = 13.9 millimeter.

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

Plugging the values

Area of sector = [tex]\frac{133}{360} * 3.14 * (13.9)^{2}[/tex].

Area of sector = [tex]\frac{133}{360} * 3.14 * 193.21[/tex].

Area of sector = [tex]\frac{133}{360} * 606.6794[/tex].

Area of sector = [tex]\frac{80688.3602}{360}[/tex].

Area of sector = 224.134333889 mm²

Area of sector = 224.2 mm² ( nearest tenth)

Therefore, Area of sector = 224.2 mm².

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