SOLUTION: The area of a sector of a circle with the radius 7cm is 15 square cm. Find the measure of the central angle of the sector in degrees.
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Question 966649: The area of a sector of a circle with the radius 7cm is 15 square cm. Find the measure of the central angle of the sector in degrees.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the area of a sector is equal to x / 360 * pi * r^2.
your area is 15 square cm.
your radius is equal to 7 cm.
the formula becomes 15 square cm = x / 360 * pi * 7^2
solve for x to get x = 15 * 360 / pi / 7^2 which becomes x = 35.07904868 degrees.
to see if that's correct, go back to the original formula and replace x with 35.07904868 and solve for the area to see is you get 15 square cm.
the formula is:
A = x/360 * pi * r^2
x = 35.07904868
r = 7
r^2 = 49
formula becomes A = (35.07904868 / 360) * pi * 49
solve for A to get A = 15.
solution is confirmed as good.
angle = 35.07904868 degrees.
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