anonymous
  • anonymous
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?
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
no more drawings this time
anonymous
  • anonymous
I got pi cubed/4
anonymous
  • anonymous
yep

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anonymous
  • anonymous
so how could I rewrite this?
anonymous
  • anonymous
rewrite what?
anonymous
  • anonymous
pi cubed/4
anonymous
  • anonymous
I need to rewrite as a times pi to the b power
anonymous
  • anonymous
So, the area is π³/4. Rewrite it as π³/4 = aπ^b. Find the a and b.
Mr.Math
  • Mr.Math
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 \(ab=\frac{3}{4}\).
anonymous
  • anonymous
ok
anonymous
  • anonymous
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

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