The volume of a cylinder (think about the volume of a can) is given by V = πr2h where r is the radius of the c

Question

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.




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.






c) Graph this function.

Answer 1

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

V= 100 = π r^2 h
then r^2 = 100/ π h
so r = 10/ sqrt(πh).

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.
100 = π (4) h
then h = 100/4π = 7.957 about 8.

Answer 2

Just get h on one side:
V=pi*r-squared*height
V/h=pi*r^2
h=(pi*r^2)/V, or
h=(pi*r^2)/100 if volume is constant.

b.

h=pi*2cm^2/100

h=.126cm

c. I can't graph it here. But just set it up so that X=height andY=radius, assuming the volume stays the same: