SOLUTION: Find the exact perimeter (in centimeters) and area (in square centimeters) of the sector whose lengths are 16cm and radius is 135 degrees

Question 1194249: Find the exact perimeter (in centimeters) and area (in square centimeters) of the sector whose lengths are 16cm and radius is 135 degrees
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52790) (Show Source): You can put this solution on YOUR website!
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Find the exact perimeter (in centimeters) and area (in square centimeters) of the sector
whose lengths are 16cm and radius is 135 degrees
~~~~~~~~~~~~~~~~~~

For your info: degree is not a measure unit for radius.

Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

It sounds like the radius is 16 cm and the central angle is 135 degrees.

A full circle of radius 16 cm has the exact circumference of 2pi*r = 2*pi*16 = 32pi cm.

However, we only want a fractional pizza slice of this. We want 135/360 = 3/8 of the full thing.
(3/8)*(full circumference) = (3/8)*(32pi) = 12pi

The curved portion is exactly 12pi centimeters.
Add on the two straight line portions of the pizza slice
12pi + 16 + 16 = 12pi + 32

The perimeter of this pizza slice is exactly 12pi + 32 centimeters.

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The area of a full circle of radius r = 16 is
A = pi*r^2
A = pi*16^2
A = 256pi

Take 3/8 of it to get the area of the pizza slice
(3/8)*256pi = 96pi

Area of the sector = 96pi square cm.

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