1. Geometry-Circle-Cylinder help

Hi, I'm having trouble with this problem. I've worked it, and my answer keeps getting flagged as incorrect:

By what percent is the area of a 12.4- cm-radius circle increased if the radius is increased 1.0 cm?

I come up with 16.8% using pi(r^2) and dividing the difference by 12.4's area. Thanks in advance!

2. Hello, clockworks204!

Looks good to me!

3. Originally Posted by clockworks204
Hi, I'm having trouble with this problem. I've worked it, and my answer keeps getting flagged as incorrect:

By what percent is the area of a 12.4- cm-radius circle increased if the radius is increased 1.0 cm?

I come up with 16.8% using pi(r^2) and dividing the difference by 12.4's area. Thanks in advance!
If the radius of $\displaystyle 12.4\,\textrm{cm}$ is increased by $\displaystyle 1\,\textrm{cm}$, then the radius becomes $\displaystyle 13.4\,\textrm{cm}$.

This means

$\displaystyle 12.4k = 13.4$

$\displaystyle k = \frac{13.4}{12.4}$

$\displaystyle = \frac{134}{124}$

$\displaystyle = \frac{67}{62}$.

So the magnification factor of the radius is $\displaystyle \frac{67}{62}$.

This means the magnification factor of the area is

$\displaystyle k^2 = \left(\frac{67}{62}\right)^2$

$\displaystyle = \frac{4489}{3844}$

$\displaystyle \approx 1.16779$

$\displaystyle = 116.779\%$.

Since you end up with $\displaystyle 116.779\%$ of what you started with, the area has increased by $\displaystyle 16.779\%$.

4. Thank you all for explaining. I did have the right answer rounded, but the LONCAPA program would only accept 16.779 as an answer!