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rates of change question

Stuck on this question. I formed an equation of dA/dt=dA/dr * dr/dt.
I know dA/dr is 8*pi*r. But i dont know how to work out dr/dt.

QUESTION: The volume of a sphere is decreasing at a rate of 60mm^3s^-1. Find the rate of decrease of the surface area when the volume is 800mm^3.
Reply 1
Original post by fiftythree
Stuck on this question. I formed an equation of dA/dt=dA/dr * dr/dt.
I know dA/dr is 8*pi*r. But i dont know how to work out dr/dt.

QUESTION: The volume of a sphere is decreasing at a rate of 60mm^3s^-1. Find the rate of decrease of the surface area when the volume is 800mm^3.

You are given that dV/dt = -60. Have you tried using that?
Original post by fiftythree
Stuck on this question. I formed an equation of dA/dt=dA/dr * dr/dt.
I know dA/dr is 8*pi*r. But i dont know how to work out dr/dt.

QUESTION: The volume of a sphere is decreasing at a rate of 60mm^3s^-1. Find the rate of decrease of the surface area when the volume is 800mm^3.


Note that volume of a sphere radius rr is V=43πr3V = \dfrac{4}{3}\pi r^3. Therefore, dVdr=4πr2\dfrac{dV}{dr} = 4\pi r^2.

We are told that dVdt=60\dfrac{dV}{dt} = -60 hence dVdrdrdt=60\dfrac{dV}{dr}\dfrac{dr}{dt} = -60.

When V=800V=800, what is rr??

Hence, what is dVdr\dfrac{dV}{dr} ?

Hence, what is drdt\dfrac{dr}{dt} ?
Reply 3
Original post by RDKGames
Note that volume of a sphere radius rr is V=43πr3V = \dfrac{4}{3}\pi r^3. Therefore, dVdr=4πr2\dfrac{dV}{dr} = 4\pi r^2.

We are told that dVdt=60\dfrac{dV}{dt} = -60 hence dVdrdrdt=60\dfrac{dV}{dr}\dfrac{dr}{dt} = -60.

When V=800V=800, what is rr??

Hence, what is dVdr\dfrac{dV}{dr} ?

Hence, what is drdt\dfrac{dr}{dt} ?

Thanks I solved it

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