# What is wrong with this circle's area problem?

My solution and my book's solution don't match.

Is something wrong with the my solution?
If so, where and why?

My book says:

The radius r of a circle increases by 50%.
In terms of r, what is the area of the circle

My solution:

1. A = $\pi r^2\$ => Area of any circle
2. ir = $\ 3r/2 \$ => Increased radio
3. A$\ _{ir} = \pi ir^{2} \$ => Area of circle with increased radio
4. A$\ _{ir} = \pi (3r/2 )^{2} \$ => Substituting ir with its value
5. A$\ _{ir} = \pi (9r^2/4 ) \$ => Square
6. A$\ _{ir} = \ (9\pi r^2 )/4 \$ => Result

Is the In terms of r tricky?

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What's the solution from your book? – draks ... Oct 9 '12 at 14:25
@draks: thanks for the interest, the book says: $\ (4\pi r^2 )/3 \$ – user454322 Oct 9 '12 at 14:30
@EmmadKareem: thanks. Not sure what does "Increased ratio" means, that is what the problem says. I am assuming that means 3r/2. – user454322 Oct 9 '12 at 14:31
your book is wrong... – draks ... Oct 9 '12 at 14:32
Well.....it took me a while, and I was getting crazy. The truth is that: I was looking at the wrong solution, the book is right...so embarrassed – user454322 Oct 12 '12 at 16:19