One last physics problem?

Question

Air is blown into a spherical balloon so that, when its radius is 6.60 cm, the rate at which the volume of the balloon increases is 536.4 cm cubed per second and remains constant.Finally the rate at which the radius increases is 0.24 cm cubed per second.

Explain physically why the rate at which the radius increases is larger or smaller than 0.980 cm/s

Answer 1

I'm not sure this question has been posted correctly, or whether it was given to you correctly in the first place.

The radius can only ever increase in cm per second, not cm cubed per second, only the volume will increasein cm cubed per second.  

You've already stated that the radius increases at a rate of 0.24 cm cubed per second (this is the part I'm having trouble with - it looks like a trick question in its present form.

You'll have to clarify exactly what it says, word-for-word, in the question you've been given.  

Update:  Thanks for the extra information, but it still doesn't clarify the question in a way which would allow me to give you a definitive answer.

The volume of a sphere is calculated as follows:

V = 4/3 pi r^3

That's (4/3) times (pi) times (radius cubed)

4/3 doesn't change, that's a constant, pi doesn't change, that's a constant

If the volume increases constantly then r^3 must also change constantly.  Take the cube root of r^3 and you'll have the radius.  To get the value by which the radius changes over time you need the first volume and the second volume, get teh r^3 values and divide by the time taken (which you must have been given) to see whether the change is larger or smaller than 0.98cm/s

There's a cube root calculator here for you to use

http://www.csgnetwork.com/cuberootcubeca...