Question

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

Answer 1

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

Answer 2

2pir^2+2pirh?

Answer 3

oh wait
just pir^2?

Answer 4

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?

Answer 5

2pirh?

Answer 6

is the answer 4.06?

Answer 7

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.

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

359=2pir^2 + 20pir?

Answer 13

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.

Answer 14

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

Answer 15

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

Answer 16

after that step i'm getting very confused

Answer 17

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

Answer 18

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

Answer 19

quadratic formula?

Answer 20

okay thank you

Answer 21

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

Answer 22

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

Answer 23

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)

Answer 24

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

Answer 25

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

Answer 26

114.27325

Answer 27

am i calculating this right

Answer 28

i feel so wrong

Answer 29

yes, not correct.

Answer 30

what am i doing wronnggggg

Answer 31

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)

Answer 32

-28.56831228

Answer 33

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 ?

Answer 34

i'm getting -118.5465.

Answer 35

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

Answer 36

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

Answer 37

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

Answer 38

OHHHHHHH, 328.5465

Answer 39

i forgot the other minus

Answer 40

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

now find the square root.

Answer 41

4.062925852??????

Answer 42

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

Answer 43

yes, 4.06

Answer 44

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

Answer 45

Sorry I wasn't able to help you through it

Answer 46

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

Answer 47

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

Answer 48

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

Answer 49

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.