Question

Is this the correct answer?

"The formula for the surface area or a sphere is: SA = 4pi*r^2. If a snowball melts so that its SA decreases at a rate of 1cm^2/min, find the rate at which the radius decreases when the diameter is 1 meter.

Any and all help is greatly appreciated!

Answer 1

HI!! ( again )

Answer 2

\[S=4\pi r^2\\
S'=8\pi rr'\]

Answer 3

\[\frac{dr}{dt} = \frac{1}{400\pi} cm/\min\]

Answer 4

your are told \(S'=1\) put \[1=8\pi rr'\] solve for \(r'\)

Answer 5

if the diameter is \(1\) then the radius is \(\frac{1}{2}\)

Answer 6

so no, i don't think that answer is correct

Answer 7

oooh i see
the units have changed doe

Answer 8

very tricky

Answer 9

ok now your answer looks a lot better

Answer 10

\[1=8\times 50\pi r'\] so yeah

Answer 11

Here's what I did:
\[SA = 4\pi*r^2\]
\[\frac{dSA}{dt} = 4\pi*2r*\frac{dr}{dt}\]
\[(1cm^2/\min) = 4\pi(2*50cm)*\frac{dr}{}\]
\[1 = 400\pi*\frac{dr}{dt}\]
\[\frac{dr}{dt} = \frac{ 1 }{400\pi}\]

Answer 12

Is that wrong? :/

Answer 13

yeah right
lot easier to write \(r'\) instead of \(\frac{dr}{dt}\) but yes you are correct
i did not notice they changed the units from cm to mm
very tricky (well not really, if i knew how to read carefully)
you are right as far as i can see

Answer 14

Thanks again misty;)

Answer 15

\[\color\magenta\heartsuit\]