Question

Water is pouring into a right circular cone with altitude=12 inches and diameter=4 inches. Which formula below would correctly measure the rate at which the volume is increasing when the altitude is h inches and the altitude is growing at a rate of dh/dt.

I know the answer is: dV/dt=1/36(pi)(h)^2(dh/dt) but i need to figure out how to get there.

Answer 1

Water is pouring into a right circular cone
with altitude=12 inches
and diameter=4 inches.

Which formula below would correctly measure
the rate at which the volume is increasing
when the altitude is h inches
and the altitude is growing at a rate of dh/dt.

What is the formula for the volume of a cone?

Answer 2

V=(1/3)(pi)r^2h

Answer 3

then we just need to put that thru a derivative to get:

V' = (1/3) 2pi r r' dh/dt

V' = (2pi r/9) r' dh/dt

it looks like they recalculated r in terms of h

Answer 4

r/h = (4/2)/12

r = h/6

V=(1/3)(pi) r^2 h

V=(1/3)(pi) (h/6)^2 h

V=(1/3)(pi) h^3/36

V' =(3pi/3)(pi) (h^2/36) dh/dt