The volume of a cylinder (think about the volume of a can) is given by V = pi r2h where r is the radius of the cylinder and h is the height of the cylinder

The volume of a cylinder (think about the volume of a can) is given by V = πr2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 100 cubic centimeters.

a) Write h as a function of r. Keep "" in the function's equation.

We know that V = 100, so plug that in for V, and solve the equation for r:

100 = πr2h
100/(πh) = r2
r = √100/πh
r = 10/(√πh)

Usually when you take the square root of something, you have 2 answers - a positive one and a negative one. However, this equation describes the radius, which is a length, and therefore can't be negative.

b) What is the measurement of the height if the radius of the cylinder is 2 centimeters? Round your answer to the nearest whole number.

Plug r = 2 into the equation we found in part a, then solve for h:

r = 10/(√πh)
2 = 10/(√πh)
1/5 = 1/(√πh)
5 = √πh
25 = πh
h = 25/π = 7.96

please see the attached file.