# Geometry-Circle-Cylinder help

• Jun 3rd 2010, 04:52 PM
clockworks204
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!
• Jun 3rd 2010, 05:24 PM
Soroban
Hello, clockworks204!

Looks good to me!

• Jun 3rd 2010, 05:36 PM
Prove It
Quote:

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 $\displaystyle 16.779\%$.
• Jun 4th 2010, 03:38 AM
clockworks204
Thank you all for explaining. I did have the right answer rounded, but the LONCAPA program would only accept 16.779 as an answer!