Question

A circle with radius 12 cm has a segment with a central angle of 60. What is the area of the segment?​

Answer 1

Answer:

Exact Area = 24pi square cm

Approximate Area = 75.36 square cm  (when using pi = 3.14)

Note: "square cm" can be abbreviated to "cm^2" without quotes.

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Explanation:

Let's find the area of the full circle with radius r = 12

A = pi*r^2

A = pi*12^2

A = 144pi  

This is the exact area of the full circle in terms of pi. To get the approximate area, you would replace pi with something like 3.14 (though you could use more decimal digits in pi to get a more accurate area).

We found the area of the full circle, but we only want a pie slice of it. Each slice is 60 degrees, out of 360 total. So that means we want 60/360 = 1/6 of the full area.

In other words, there are 6 slices because 360/60 = 6, which means we'll divide the area we got by 6

(144pi)/6 = (144/6)pi = 24pi

The exact area of the pie slice is 24pi square cm

If you used the approximation pi = 3.14, then that leads to an approximate answer of 24*pi = 24*3.14 = 75.36 square cm