Question

How does the volume of a sphere compare to that of the volume of a cylinder? What would you say the scale factor for Vol sphere:Vol cylinder

Answer 1

The volume of a sphere is 2/3 times the volume of a similar cylinder

Scale factor : 2/3

Explanation:

Let us consider a sphere of radius r. The volume of the sphere will be given as

`V_(s)=(4)/(3) \pi r^(3)`

Similarly, let us consider a cylinder with its height being twice the radius of the sphere. We will have its volume given as:

`V_(c)=\pi r^(2)h`

but h = 2r

Hence we have

`V_(c)= 2\pi r^(3)h`

We can divide the two volumes to get a constant that links them together

`(V_(s))/(V_(c))=((4)/(3) \pi r^(3))/(2\pi r^(3)h)`

this will give us 2/3

Hence the scale factor for Vol sphere: Vol cylinder is 2/3