Diffrentiation ( rates of change)?

Question

The volume of a cylinder increases at a rate of 1.0cm^3 per second. The height, h cm, of the cylinder is always twice the radius, r cm. Find the rate of change in radius when the radius is 8cm.

Answer 1

you might wanna check again to see if it says cylinder or cone, cause there wouldn't be a change in rate of radius if its a cylinder

Answer 2

h = 2r

Volume, V = π r² h = π r² *(2r)

=> V = 2 π r³

=> dV/dt = 6 π r² dr/dt

=> dr/dt

= (dV/dt) / (6π r²)

= (1) / (6π*(8)²)

= 8.3 x 10^(-4) cm/s.

Answer 3

dV/dt=1

But V=pi r^2 h

= pi r^2 2r (since h=2r)

= 2pi r^3

dV/dt = 2pi 2r^2 dr/dt

=> 1 = 2pi r^2 dr/dt

=> 1 = 2pi (8)^2 dr/dt

=> dr/dt = 1/(128pi)