6 replies to this topic

[RhetoricalRuvim]

Hello. Sorry if this is the wrong forum to post, but I have a calculus homework problem, and for some reason I'm getting the wrong answer. It's about related rates.

Here's what the problem says:

The radius of a sphere is increasing at a rate of 9 mm/sec. How fast is the volume increasing when the diameter is 130 mm? 

V= 4/3*pi*r^3

Here's my work:

dr/dt = 9 (mm/s) 

dV/dt ? @ r=65 


dV/dt = 4/3 * pi * 3*r^2*dr/dt 

dV/dt = 4 * pi * (65)^2 * (9) 

dV/dt = 477836.2426 

But the problem is, the right answer - at least according to the teacher's key - is 477.8 , which is about 10^(-3) the size of my answer.

What am I doing wrong?

[WingedPanther]

What are the units on the teacher's key? Your logic looks right, but that 10^-3 feels a bit too convenient.

[RhetoricalRuvim]

I'm not sure what the units were. The assignment also says to give the answer in both cm and mm, and I'm not sure about which the teacher used.

[irancplusplus]

Hi
The unit of your answer in http://latex.codecog...\frac{mm^3}{s}. And

http://latex.codecog...}\frac{cm^3}{s}

[RhetoricalRuvim]

Wait, but # of cm * 10 is # of mm, right?

[irancplusplus]

1 cm = 10 mm
so
http://latex.codecogs.com/gif.latex?1 mm =\frac{1}{10} cm
and
http://latex.codecog...ac{1}{1000}cm^3

[RhetoricalRuvim]

Oh, I forgot about cubing the bottom part of the fraction.

Let's see, now, 477836.24 mm^3 / mm^3 * 1/1000 cm^3 = 477836.24 * 1/1000 cm^3 = 477836.24 / 10^3 cm^3 = 477.8 cm^3

That would make sense why the teacher's answer was what it was; it was probably in centimeters cubed, and the answer I had is in millimeters cubed.

Thanks guys.