Question

A paper cup has the shape of a cone with height 8cm and radius 3cm at the top. Water is being poured into the cup at the rate of 2cm3/s. How fast is the water level rising when the water is 6cm deep?

Answer 1

1. Express r in terms of h:
r=3/8h
2. Express volume in terms of h:
V=(1/3)πr²h
=(1/3)π(3h/8)²h
=(3π/64)h³
dV/dh=(9π/64)h²
dV/dt=2 cm³s^-1

dh/dt
=(dV/dt)/(dV/dh)
=2*64/(9πh²)
=128/(9πh²)
=0.1257 cm-s^-1

Answer 2

thank you .