Answer:
Volume of cylinder is thrice the volume of cone.
Step-by-step explanation:
Given:
Diameter of cone and cylinder, [tex]d=10\textrm{ in}[/tex]
Height of cone and cylinder, [tex]h=12\textrm{ in}[/tex]
Radius of cone and cylinder, [tex]r=\frac{d}{2}=\frac{10}{2}=5\textrm{ in}[/tex]
Volume of a cylinder is given as, [tex]V_{cyl}=\pi\times r^{2}\times h=3.14\times (5)^{2}\times 12=942\textrm{ }in^{3}[/tex]
Volume of a cone is given as, [tex]V_{cone}=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times 3.14\times (5)^{2}\times 12=314\textrm{ }in^{3}[/tex]
Now, the ratio of volume of cylinder to volume of cone is given as:
[tex]\frac{V_{cyl}}{V_{cone}}=\frac{942}{314}=3\\\\\therefore V_{cyl}=3V_{cone}[/tex]
Hence, volume of a cylinder is thrice the volume of a cone for the same height and diameter.
