SOLUTION: What is the area of the shaded figure below if the measure of the central angle is 30° and the radius is 10 cm?

Question 1190251: What is the area of the shaded figure below if the measure of the central angle is 30° and the radius is 10 cm?

Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

Normally when there are diagrams that accompany text, I would request the student to please post the diagram.

However, based on the description you wrote out, there appears to be enough information to answer the question.

A full circle has area of A = pi*r^2
Plug in the radius r = 10 to find that the exact area is 100pi square cm.

Assuming you want a 30 degree pizza slice of the full circle, then you want 30/360 = 1/12 of the full area
In other words, cut the pizza into 12 equal slices, and only shade one slice to represent the fraction 1/12.

So (1/12)*100pi = (25/3)pi square cm represents the exact area of the pizza slice.
Replace pi with something approximate like 3.14 and you'll get the approximate area.
Use more decimal digits of pi to get a more accurate value (though it won't be perfectly exact).

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