The area of a sector of a circle with a central angle of 15π rad is 18 m².
Find the radius of the circle.
I set up my equation as:
18m^2=(1/2)(r^2)(1/5 pi)
i isolate r^2 by dividing both sides by (1/2) and (1/5 pi, getting:
180pim^2=r^2
i then take the square root of each and get 13.4164 pi=r
this is a problem, because i am using WAMAP and it does not allow decimal approximations and it wants pi left in the answer. did i go wrong somewhere? thanks
well, if you have pi/10 r^2 = 18, you wind up with
r^2 = 180/pi
r = 3√(20/pi)
Now, if your angle is 1/(5pi), then you are correct to have r^2 = 180pi
But, √(180pi) is not √180 * pi. When you take the root, you also have to include pi inside: √(180pi) = 3√(20pi).
To solve the equation and find the radius of the circle, you set up the equation correctly. However, there is a calculation mistake in simplifying the equation.
Starting with:
18m² = (1/2)(r²)(1/5π)
Divide both sides by (1/2) and (1/5π):
((1/2)(r²)(1/5π)) / ((1/2)(1/5π)) = (18m²) / ((1/2)(1/5π))
Simplify the right side:
r² = (18m²) / ((1/2)(1/5π))
= (18m²) / ((1/10)π)
= (180m²) / π
Take the square root of both sides:
√(r²) = √((180m²)/π)
Simplify the right side:
r = √((180m²)/π)
Now, you need to leave the answer in terms of π. To do that, you can simplify the radical as follows:
r = √((180m²)/π)
= √((180/π)m²)
= √(180/π) * √m²
= √(180/π) * m
Therefore, the radius of the circle is √(180/π) times the given unit of length (in this case, meters). This is the exact answer, leaving π in the expression.