Question

Two cylinders, a and b, each started with different
amounts of water. The graph shows how the height of
the water changed as the volume of water increased in
each cylinder.
Which cylinder has the larger radius? A or B?
Explain how you know.

Answer 1

Using implicit differentiation, it is found that cylinder B has the larger radius.

What is the volume of a cylinder?

The volume of a cylinder of radius r and height h is given by:

$V = \pi r^2h$

Applying implicit differentiation, the rate of change is given by:

$\frac{dV}{dt} = \pi\left(2rh\frac{dr}{dt} + r^2\frac{dh}{dt}\right)$

The rate of change of the height is given by:

$r^2\pi\frac{dh}{dt} = \frac{dV}{dt} - 2rh\pi\frac{dr}{dt}$

$\frac{dh}{dt} = \frac{1}{r^2}{\pi}\left(\frac{dV}{dt} - 2rh\pi\frac{dr}{dt}\right)$

That is, a larger radius leads to a smaller rate of change of the height, hence from the graph cylinder B has the larger radius.

More can be learned about implicit differentiation at https://brainly.com/question/25608353