The formula of a volume of a cylinder:
[tex]V_{cylinder}=\pi r^2H[/tex]
r - radius
H - height
We have the diameter d = 8 in and height H = 9 in.
[tex]d=2r\to r=d:2\to r=8\ in:2=4in[/tex]
Substitute:
[tex]V_{cylinder}=\pi(4^2)(9)=\pi(16)(9)=144\pi\approx144\cdot3.14=452.16\ in^3[/tex]
The formula of a volume of a cone:
[tex]V_{cone}=\dfrac{1}{3}\pi r^2H[/tex]
r - radius
H - height
We have the diameter d = 8 in → r = 4 in and the height H = 18 in.
Substitute:
[tex]V_{cone}=\dfrac{1}{3}\pi(4^2)(18)=\pi(16)(6)=96\pi\approx96\cdot3.14=301.44\ in^3[/tex]
[tex]\dfrac{V_{cylinder}}{V_{cone}}=\dfrac{452.16}{301.44}=1.5[/tex]
The volume of the cylinder is one and a half times larger than the volume of the cone.
If the cylinder and the cone have equal radii and heights then the volume of the cylinder is three times greater than the volume of the cone.
[tex]V_{cone}=\pi r^2H\\\\V_{cylinder}=\dfrac{1}{3}\pi r^2H\\\\\dfrac{V_{cylinder}}{V_{cone}}=\dfrac{\pi r^2H}{\frac{1}{3}\pi r^2H}=\dfrac{1}{\frac{1}{3}}=3[/tex]
