Question

If the area of a circle whose diameter is pi, is written

as a times pi to the b power, what is the value of

ab?

Answer 1

no more drawings this time

Answer 2

I got pi cubed/4

Answer 3

yep

Answer 4

so how could I rewrite this?

Answer 5

rewrite what?

Answer 6

pi cubed/4

Answer 7

I need to rewrite as a times pi to the b power

Answer 8

So, the area is π³/4. Rewrite it as π³/4 = aπ^b. Find the a and b.

Answer 9

You know the area of a circle is \(\pi r^2\), where \(r\) is the radius of the circle. In this case we have \(r=\frac{\pi}{2}\). Thus the area, call it \(A\), is \(A=\pi(\frac{\pi}{2})^2=\frac{1}{4}\pi^3.\)
Now if we set this \(A=a\pi^b=\frac{1}{4}\pi^3.\) Then we have \(a=\frac{1}{4}\) and \(b=3\). So \(ab=\frac{3}{4}\).

Answer 10

ok

Answer 11

You asked me why a should be 1/4, not 4. It's because 4 is in denominator, so it is 1/4.
π³/4 = (1/4)π³