anonymous
  • anonymous
a can of beans has surface area 359 cm^2. Its height is 10 cm. What is the radius of the circular top?
Mathematics
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anonymous
  • anonymous
a can of beans has surface area 359 cm^2. Its height is 10 cm. What is the radius of the circular top?
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
Do you know the formula for calculating the surface area of a sphere?
anonymous
  • anonymous
2pir^2+2pirh?
anonymous
  • anonymous
oh wait just pir^2?

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anonymous
  • anonymous
Pir^2 is just the surface area of one lid, so for the 2 lids it would be 2Pir^2 what is the formula for the walls?
anonymous
  • anonymous
2pirh?
anonymous
  • anonymous
is the answer 4.06?
anonymous
  • anonymous
im following the steps the teacher gave me for notes but i keep getting them wrong. This is the 5th problem like this I've attempted to do.
anonymous
  • anonymous
The wall of the can would be circumference x height. (The height is given). What is the circumference?
anonymous
  • anonymous
I did not calculate the answer. I'm doing step by step with you.
anonymous
  • anonymous
I apologize, you wrote the correct answer earlier. The surface area of the wall is 2 pirh.
anonymous
  • anonymous
And what you wrote the very first time "2pir^2+2pirh" is also correct.
anonymous
  • anonymous
359=2pir^2 + 20pir?
anonymous
  • anonymous
So far looks good. It may be easier to factor out a 2 and write it as 359 = 2 (pir^2 + 10pir). You're on the right track.
anonymous
  • anonymous
in my notes my teacher has me equal it out to 0 following this it would be 0 = 2pir^2+20pir-359
phi
  • phi
this one is more painful than that. How about divide all term by 2pi and write it as \[ r^2 + 10 r - \frac{359}{2 \pi} = 0 \] if we use a calculator, that is about \[ r^2 + 10 r - 57.1366=0 \] to find r we could use the quadratic formula
anonymous
  • anonymous
after that step i'm getting very confused
anonymous
  • anonymous
Give me a few minutes. I'll try it the way you have it in your notes.
anonymous
  • anonymous
x=-b+- sqr rt, b^2-4ac / 2a
anonymous
  • anonymous
quadratic formula?
anonymous
  • anonymous
okay thank you
phi
  • phi
yes, quadratic formula. if you first divide by 2pi most of the numbers get a bit smaller and you would have a=1, b=10 , c= 57.1366
anonymous
  • anonymous
-10pi+- sq rt. 100-4(!)(57.1366)/2?
phi
  • phi
if you are doing \[r^2 + 10 r - 57.1366=0 \] -b is -10 (not -10pi) a=1 so 4ac is just 4*-57.1366 (notice c is negative)
phi
  • phi
so \[ \frac{-10+ \sqrt{100 + 228.5465}}{2} \]
phi
  • phi
I would pick the + sqrt because otherwise we get a negative radius
anonymous
  • anonymous
114.27325
anonymous
  • anonymous
am i calculating this right
anonymous
  • anonymous
i feel so wrong
phi
  • phi
yes, not correct.
anonymous
  • anonymous
what am i doing wronnggggg
phi
  • phi
can you get this far: \[ \frac{-10+ \sqrt{100 + 228.5465}}{2}\] (by the way for c = -359/(2pi) I would use all the digits the calculator has)
anonymous
  • anonymous
-28.56831228
phi
  • phi
for \[ r^2 + 10 r - 57.1366=0 \] a=1, b=10, c= -57.1366 (roughly) let's first figure out b^2 -4 * a *c that is 100 - 4 * 1 * -57.1366 what does that simplify to ?
anonymous
  • anonymous
i'm getting -118.5465.
phi
  • phi
4*-57.1366= -228.5465 now do 100 - (-228.5465)
anonymous
  • anonymous
I made a mistake in my calculation. I don't want to post until I figure out where the error is.
phi
  • phi
notice it is minus a minus. that makes it a +
anonymous
  • anonymous
OHHHHHHH, 328.5465
anonymous
  • anonymous
i forgot the other minus
phi
  • phi
yes. so make a note: Be careful about the minus signs (they are evil) now find the square root.
anonymous
  • anonymous
4.062925852??????
phi
  • phi
yes, that looks good. do they want the answer rounded ?
anonymous
  • anonymous
yes, 4.06
anonymous
  • anonymous
so i was right earlier. Thank you both so much for your help!
anonymous
  • anonymous
Sorry I wasn't able to help you through it
phi
  • phi
if we use 4.06 in the original formula we get 358.67 or about 359, so it checks out.
anonymous
  • anonymous
If it helps I'll post how to do it in a calculator that has fractions
anonymous
  • anonymous
\[\frac{ -20 + \sqrt{20^2+ 8(\frac{ 359 }{ \pi })} }{ 4 }\]
anonymous
  • anonymous
If your calculator allows you to enter the above equation (in one step) you'll get the same answer. I put in + 8 since the two negatives become positive.

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