A cylinder and a cone have the same diameter: 10 inches. The height of the cylinder and the cone is the same: 12 inches. Use π = 3.14. What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work. (10 points)

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.