need help writting a funtions equation.?

Question

need to write a funtion equation for the volume of a cylinder. v=pi r2h, r is the radius, h is the height and the volume is 100 cubic cent. I need to write h as a funtion of r. and keep pi in the funtion equation and then find the measurement for the height of the radius of the cylinder 2 centimenters and round to nearest whole # I have not clue. what this means. help

Answer 1

v = (pi)(r^2)h but v=100 cm^3

so 100 = (pi)(r^2)h
rearrange:
h = 100/((pi)(r^2))
now h is a function of r. This means the value of h is dependent on the value of r as everything else in the equation is a constant.
so with r=2cm
h = 100/(4(pi)) = 25/(pi) = 32 cm to the nearest whole

Answer 2

The volume of a cylinder, as you said, is the formula

V = pi*r^2*h

To write h as a function of r, all you have to do is solve for h. This is done by dividing both sides by pi*r^2

h = V/(pi*r^2)

Now, you have your volume (V = 100), and you have your radius (2). All you have to do is plug in those values for your new equation.

h = 100/(pi*2^2) = 100/(4pi) = 25/pi