(1/3) × the cone's volume = The cylinder's volume.
Step-by-step explanation:
Step 1:
The volume of any cone is obtained by multiplying [tex]\frac{1}{3}[/tex] with π, the square of the radius ([tex]r^{2}[/tex]) and the height ([tex]h[/tex]).
So the volume of the cone, [tex]V=\pi r^{2} \frac{h}{3}[/tex].
Step 2:
The cylinder's volume is nearly the same as the cone but instead by multiplying [tex]\frac{1}{3}[/tex] we multiply with 1.
So the cylinder's volume is determined by multiplying π with the square of the radius of the cylinder ([tex]r^{2}[/tex]) and the height of the cylinder ([tex]h[/tex]).
So the the cone's volume, [tex]V = \pi r^{2} h[/tex].
Step 3:
Now we equate both the volumes to each other.
The cone's volume : The cylinder's volume = [tex]\pi r^{2} \frac{h}{3}: \pi r^{2} h[/tex] = [tex]\frac{1}{3} : 1[/tex].
So if we multiply the cone's volume with [tex]\frac{1}{3}[/tex] we will get the cylinder's volume with the same dimensions.
