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you have forgotten the pi

divide by pi then should be correct

Oh, alright thanks

Take note of your units.

If you write -3cm³/s on the LHS then for your RHS, your radius should have a cm

Oh ok, thanks

i.e

dv/dr = dr/dt × dv/dt

-3 cm³/s = dr/dt × 4πr²

-3 cm³/s = dr/dt × 4π(1.2 cm)²

-3 cm³/s = dr/dt × 5.76π cm²

dr/dt = -3cm³/s / 5.76π cm²

≈ -0.16579 cm/s

= -0.166 cm/s (3s.f)

It is a rate of change of radius so in your original working, having it in terms of volume (cm³/s) wouldn't make sense.

This occurred because the cm was omitted when evaluating 4πr²

(the 1.2 cm would have been squared to become 1.44 cm², and then multiplied by 4π to become 5.76π cm². This cm² is then cancelled out by the cm³ on the LHS when you divide the LHS by it, leaving an overall unit of cm/s)

Noted thanks

By the way, the asked for 'what is the rate that the radius decreasing ... ...'

So if your final answer is -0.166 cm/s it would be wrong since decreases cannot be negative, i.e they are an absolute value.

In contrast, dr/dt is a rate of of change , and change can be positive or negative.


A correct final answer would be :

'The radius is decreasing at 0.166 cm/s (3s.f)'

Oh right, thanks for the detailed explanation.

No prob