Question

If a snowball melts so that its surface area decreases at a rate of 1 cm2/min, find the rate at which the diameter decreases when the diameter is 9 cm. (Give your answer correct to 4 decimal places.)

Answer 1

@Science_ALLY

Answer 2

you need to equations, one for surface area and one for volume. then you'll need to differentiate with respect to time (each one).

Answer 3

i think I only need surface area to solve this

Answer 4

Okay.

Answer 5

A cone is a spherical shape is it not? So whats the surface area of a sphere.

Answer 6

2pir^(2)

Answer 7

yeah, just surface area\[A=4 \pi r^2 \Rightarrow \frac{ dA }{ dt }=8 \pi r \frac{ dr }{ dt }\]

Answer 8

you want \[2\frac{ dr }{ dt }\]

Answer 9

And you're looking for the rate at which the diameter decreases. r = \(\frac{D}{2}\)

Answer 10

\[\frac{ dA }{ dt }=1\frac{ cm^2 }{ \min }\]

Answer 11

\[\frac{ dD }{dt }=\frac{ dA }{ dt }\cdot \frac{ 1 }{ 2 \pi\cdot 9\,\, cm }\]

Answer 12

@pgpilot326 I tried that and that answer doesn't work ):

Answer 13

\[A=4\pi r^2 = \pi D^2 \Rightarrow \frac{ dA }{ dt }=2\pi D \frac{ dD }{ dt }\Rightarrow \frac{ dD }{ dt }=\frac{ dA }{ dt }\cdot \frac{ 1 }{ 2\pi D }\]

Answer 14

I got it!

Answer 15

maybe sign, try negative of your answer (for decreasing)

Answer 16

I didn't put parenthesis in the right place in my calculator

Answer 17

there you go!

Answer 18

thank you!