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A piston is seated at the top of a cylindrical chamber with radius 3 cm when it starts moving into the chamber at a constant speed of 4 ​cm/s (see​ figure). What is the rate of change of the volume of the cylinder when the piston is 15 cm from the base of the​ chamber?
a) Let​ V, r, and h be the​volume, radius, and height of a​ cylinder, respectively. Write an equation relating​ V, r, and h.
b) Find the related rates equation.
c) When the piston is 15cm from the base of the​ chamber, the volume of the cylinder is changing at a rate of about

Respuesta :

ogorwyne

Answer:

1. V = πr²h

2. dv/dt = πr²dh/dt

3. dv/dt = 113.04

Step-by-step explanation:

We have these information

Radius R = 3cm

Height = h

Volume = V

We have been given dh/dt = 4cm

1.

An equation relating V, r, h

Volume of cylinder = πr²h

2.

The related rates equation

dv/dt = πr²dh/dt

dv/dt = π3²dh/dt

3. Continuing from number 2 above, we have

dv/dt = π3²dh/dt

= π9x4

= 3.14x9x4

= 113.04

These are the answers to the questions