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opus
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Homework Statement
Find the area, A, of a sector of a circle with a radius of 9 inches and a central angle of 30°.
Homework Equations
$$Area~of~a~Sector:$$
$$A=\left( \frac 1 2 \right)r^2θ$$
The Attempt at a Solution
[/B]
$$θ=30°$$
$$θ=30°\left( \frac π {180} \right)$$
$$θ=\left( \frac π 6 \right)$$
$$A=\left( \frac 1 2 \right)\left(9\right)^2\left(\frac π 6 \right)$$
$$A=\left( \frac {81π} {12} \right)$$
$$A≈21.2 in^2$$
My question:
I know that when you find the area of a space, it will be in ##units^2##. But I've always thought of it as a square- that is, one equal side multiplied by the other equal side obviously results in a squared result. However in this case, I don't see how the units for a sector of a circle are squared, as it doesn't seem like we're multiplying two things of equal value to each other.
So why is this result squared?