anonymous
  • anonymous
A certain cell has the shape of a sphere. The formulas S=4pie r^2 and V= (4/3) pie r^3 are used to compute the surface area and volume of the cell, respectively. Estimate the effect on S and V produced by 1% increase in the radius r.
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
Just replace r with (1.01r) in the formulas.
anonymous
  • anonymous
If \[s_1=4\pi{r^2}\]then \[{s_2}=4\pi{(1.01r)}^2=4\pi(1.0201)r^2=1.0201.{4\pi}r^2=1.0201s_1\]
anonymous
  • anonymous
If \[v_1=\frac{4}{3}\pi{r^3}\]then\[v_2=\frac{4}{3}\pi{(1.01r)^3}=\frac{4}{3}\pi(1.030301)r^3=1.030301v_1\]

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anonymous
  • anonymous
So the surface area increases by about 2%, and the volume by about 3%.
anonymous
  • anonymous
why are you using 1.01
anonymous
  • anonymous
The definition of 'percent increase' is \[\frac{r_2-r_1}{r_1}=0.01 \]0.01 is equivalent to 1%. We never actually calculate anything using percents - we use decimals and then convert to percent if needed. So\[r_2-r_1=0.01r_1 \rightarrow r_2 =r_1+0.01r_1\]i.e.\[r_2=1.01r_1\]
anonymous
  • anonymous
but i don't see where r2-r3 is
anonymous
  • anonymous
sorry I meant r2-r1
anonymous
  • anonymous
You need to find a second radius that will be 1% bigger than the first. The way it's defined in mathematics is called 'relative difference'. I used that definition to find the second radius. The r2-r1 bit is the difference, and dividing it by r1 gives you *relative" difference. We need it to be equal to 1%, so you set it to 0.01.
anonymous
  • anonymous
thanks for your help!!
amistre64
  • amistre64
is there a trick to posting questions? cause all I get when I press "ask" is a frozen box at the top....
anonymous
  • anonymous
if i have a problem i will click profile settings (just to change the screen) and then go back to home. that will usually fix the problem for me. my computer gets slow when I have several replies on a problem.
anonymous
  • anonymous
No problems, mom. Best way to thank me is to 'fan' me - I want to get my points up!
anonymous
  • anonymous
done!!
anonymous
  • anonymous
cheers :)

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