Question

Water is being poured into a spherical bowl of radius 4cm at a rate of 2cm3/s. How fast is the
water level rising when it is at 2cm?

Answer 1

dV/dt = 2 cm^3/s

dV/dh = surface area = pi r^2

dV/dt = dV/dh * dh/dt

so
dh/dt = dV/dt / pi r^2

so you need r, the radius of the surface 2 cm up from the bottom of the 4 cm radius sphere
I do not remember the length of a circle sector halfway from the center to the edge, look it up

Answer 2

I'm getting that r is the square root of 12, so dh/dt is 1/6pi ?

Answer 3

2/12pi = 1/(6pi) agree

Answer 4

thank you