a can of beans has surface area 359 cm^2. Its height is 10 cm. What is the radius of the circular top?

- anonymous

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- anonymous

Do you know the formula for calculating the surface area of a sphere?

- anonymous

2pir^2+2pirh?

- anonymous

oh wait
just pir^2?

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## More answers

- 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

2pirh?

- anonymous

is the answer 4.06?

- 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

The wall of the can would be circumference x height. (The height is given). What is the circumference?

- anonymous

I did not calculate the answer. I'm doing step by step with you.

- anonymous

I apologize, you wrote the correct answer earlier. The surface area of the wall is 2 pirh.

- anonymous

And what you wrote the very first time "2pir^2+2pirh" is also correct.

- anonymous

359=2pir^2 + 20pir?

- 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

in my notes my teacher has me equal it out to 0
following this it would be 0 = 2pir^2+20pir-359

- 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

after that step i'm getting very confused

- anonymous

Give me a few minutes. I'll try it the way you have it in your notes.

- anonymous

x=-b+- sqr rt, b^2-4ac / 2a

- anonymous

quadratic formula?

- anonymous

okay thank you

- 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

-10pi+- sq rt. 100-4(!)(57.1366)/2?

- 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

so
\[ \frac{-10+ \sqrt{100 + 228.5465}}{2} \]

- phi

I would pick the + sqrt because otherwise we get a negative radius

- anonymous

114.27325

- anonymous

am i calculating this right

- anonymous

i feel so wrong

- phi

yes, not correct.

- anonymous

what am i doing wronnggggg

- 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

-28.56831228

- 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

i'm getting -118.5465.

- phi

4*-57.1366= -228.5465
now do
100 - (-228.5465)

- anonymous

I made a mistake in my calculation. I don't want to post until I figure out where the error is.

- phi

notice it is minus a minus. that makes it a +

- anonymous

OHHHHHHH, 328.5465

- anonymous

i forgot the other minus

- phi

yes. so make a note: Be careful about the minus signs (they are evil)
now find the square root.

- anonymous

4.062925852??????

- phi

yes, that looks good.
do they want the answer rounded ?

- anonymous

yes, 4.06

- anonymous

so i was right earlier. Thank you both so much for your help!

- anonymous

Sorry I wasn't able to help you through it

- phi

if we use 4.06 in the original formula we get 358.67 or about 359, so it checks out.

- anonymous

If it helps I'll post how to do it in a calculator that has fractions

- anonymous

\[\frac{ -20 + \sqrt{20^2+ 8(\frac{ 359 }{ \pi })} }{ 4 }\]

- 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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