If a snowball melts so that its surface area decreases at a rate of 1 cm^2/min, ﬁnd the rate at which the diameter decreases when the diameter is 10 cm. I'm not sure where to start with this one. Help please. I'm using "S" to represent surface area and "x" for diameter.

Question

baru · Answer

whats the formula for surface are of a sphere?

baru · Answer

*surface area

azureilai · Answer

4*pi*r^2

baru · Answer

can you re-write the formula in terms of diameter?

azureilai · Answer

4*pi*(d/2)^2

azureilai · Answer

4*pi*(x/2)^2 (I forgot I was using x to represent diameter)

baru · Answer

ok
$$s=\pi (x/2)^2\simplify\s=\pi x^2$$

baru · Answer

okay?

azureilai · Answer

Where did the 4 go?

baru · Answer

$$s=\frac{4\pi x^2}{4}$$ i have just expanded the formula you gave

baru · Answer

4 and 4 cancel

azureilai · Answer

ok. I see.

baru · Answer

now differentiate both sides with respect to 't'

azureilai · Answer

So would that be
$$\frac{ ds }{ dt }=2\pi x$$

baru · Answer

u have missed out something on RHS. i said differentiate with respect to 't'. you have to assume x is a function of t (x=f(t) )

azureilai · Answer

ah so
$$\frac{ ds }{ dt }=2\pi  \frac{ dx }{ dt }$$

baru · Answer

close...but still wrong.
you have to use the 'chain rule'

$$\frac{ds}{dt}=2\pi x \frac{dx}{dt}$$

azureilai · Answer

Ok. I see where I messed up. So in the next step, do I rearrange it and plug in numbers?

baru · Answer

yep,
be careful, the question says surface area "decreases" so you have to put a minus sign :)

azureilai · Answer

Ok. Thank you very much