Answer:
The volume of a sphere is 2/3 times the volume of a similar cylinder
Scale factor : 2/3
Step-by-step explanation:
Let us consider a sphere of radius r. The volume of the sphere will be given as
[tex]V_{s}=\frac{4}{3} \pi r^{3}[/tex]
Similarly, let us consider a cylinder with its height being twice the radius of the sphere. We will have its volume given as:
[tex]V_{c}=\pi r^{2}h[/tex]
but h = 2r
Hence we have
[tex]V_{c}= 2\pi r^{3}h[/tex]
We can divide the two volumes to get a constant that links them together
[tex]\frac{V_{s}}{V_{c}}=\frac{\frac{4}{3} \pi r^{3}}{2\pi r^{3}h}[/tex]
this will give us 2/3
Hence the scale factor for Vol sphere: Vol cylinder is 2/3
