Question

A spherical snowball is melting at the rate of 2 cubic in. per minute and it's staying spherical! How fast is the radius of the snowball decreasing when the radius is 1/2 in?

Answer 1

what is the area for a sphere? i forget

Answer 2

\[\frac{3}{4}\pi r^3\] or something right?

Answer 3

think so. ya

Answer 4

well we can't guess, we need that one

Answer 5

Will check. :)

Answer 6

@satellite73 please fan me and ill fan u

Answer 7

A = 4\pi r^2

Answer 8

it is \[V=\frac{4}{3}\pi r^3\] take derivatives, you get
\[V'=4\pi r^2 r'\] you know \(V'=\frac{1}{2}, r=\frac{1}{2}\) solve for\(r'\)

Answer 9

ooops no sorry \(V'=2\)

Answer 10

so
\[2=4\times (\frac{1}{2})^2r'\] solve for \(r'\)

Answer 11

it's one right?

Answer 12

r = 2

Answer 13

oh right, r' isn't -2 because @satellite73 dropped a pi in that last comment

Answer 14

so -2 = 4 pi (1/2)^2 (r')

Answer 15

one second jigles

Answer 16

i don't know hot get the answer. im confused

Answer 17

well first try 4 (1/2)^2
1
4 * --- = 1
4
so you get -2 = pi (r') then divide both sides by pi

Answer 18

-2pi?

Answer 19

divide pi

Answer 20

by -2?

Answer 21

erm
like -2/pi instead of -2pi

Answer 22

−0.636619772368

Answer 23

yeah ... that xD

Answer 24

but in fraction form?

Answer 25

mmm depends on what your teacher wants :)

Answer 26

she wants fraction form i guess so its -2/pi for the final answer right?

Answer 27

correct! :)

Answer 28

ya, my darling is back. that's it. :)

Answer 29

let r be the radius of snow ball at any time t
\[then volume V=\frac{ 4 }{ 3 }\pi r ^{3}\]
\[\frac{ dV }{dt }=\frac{ 4 }{ 3 } \pi *3 r ^{2}\frac{ dr }{dt }\]
\[\frac{ dV }{dt }=-2 cubic inch\]
when r=1/2 inch
put the values
\[-2=4 \pi 2 ^{2}\frac{ dr }{ dt }\]
\[\frac{ dr }{dt }=\frac{ -2 }{16 \pi }=\frac{ -1 }{ 8 \pi } inch\]
negative sign shows the radius is decreasing.

Answer 30

mmm
you said r=1/2
but when you plugged it in it became "2^2" ?
@surjithayer

Answer 31

correction

\[-2=4 \pi \left( \frac{ 1 }{ 2 } \right)^{2}\frac{ dr }{dt }\]
\[\frac{ dr }{ dt }=\frac{ -1 }{\pi } inch\]

Answer 32

then how did -2 turn into -1?

Answer 33

again wrong it should be -2/ pi inch

Answer 34

okay :)
thanks for confirming :)

Answer 35

thanks for correcting me.

Answer 36

Jiggly Puff is the best!