Question

True or false? The volume of a sphere is two-thirds the volume of a cylinder with the same radius r and height 2r. Explain your reasoning.

Answer 1

You can test this like this:
by dividing the formula of the sphere on the formula of the cylinder
((4/3)*PI*r^3)/((2r*r^2*PI)=
((4/3)*r^3)/((1/3)*2r^3)=

multiply by 3 both above and under to get rid of the fraction
4*r^3/2r^3*3
4/2*3
4/6=2/3

This should work as reasoning :)