Carcass wrote:
The diameter of circle O is \(d\), and the area is \(a\).
Quantity A |
Quantity B |
\(\frac{\pi d^2}{2}\) |
\(a\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
If \(d\) = the diameter of the circle, then \(\frac{d}{2}\) = the radius of the circle.
Area of a circle \(= \pi r^2 = \pi (\frac{d}{2})^2 = \pi (\frac{d^2}{4}) = \frac{\pi d^2}{4} = a\)
So we now have:
QUANTITY A: \(\frac{\pi d^2}{2}\)
QUANTITY B: \(\frac{\pi d^2}{4}\)
If we don't already see that Quantity A is greater, we can always divide both quantities by \(\pi d^2\) to get:
QUANTITY A: \(\frac{1}{2}\)
QUANTITY B: \(\frac{1}{4}\)
Answer: A