Sal knows the volume of a cylinder is 500 cubic units. He wants to create a cylinder with twice the volume. What variation should be used?

Question

• Use the Use the same radius but double the height.
• Use the same height but double the radius.
• Double the radius and double the height.
• Use the same height but quadruple the radius.

Answer 1

The volume of cylinder is

 

V = πr²h

 

where:

r = radius

h = height

 

You know that radius and height are both directly proportion to volume.  Don't forget that radius is exponentially increased. 

 

What happens to the output when you change one independent variable and keep the other independent variable?  The volume changes at the same rate as the height.

Answer 2

Use the same radius but double the height.

 

The formula for volume of a cylinder is area of the bottom times the height, or (pi) r² h.

 

If you double the radius you would in effect have  (pi) (2r)²h = 4 (pi) r²h , meaning you would quadruple the volume.