Question

A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 3 inches. The height of the cone is 18 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.

Answer 1

Vcylinder=$\pi r^2 h$

Vcone=$\frac{1}{3} \pi r^2 h$

if we compute the volumes

given that d=8 and height cylinder=3 and height cone=18

note that d/2=r so 8/2=4=r

Vcylidner=[/tex] \pi (4)^2* 3[/tex]=$\pi (48)$=150.72 cubic inches

Vcone=$\frac{1}{3} \pi (4)^2 * 18$=$\pi (96)$=301.44 cubic inches

hmm, if we divide the volume of the cone by thhe volume of the cylinder, we get 301.44/150.72=2

so the relationship is that the cylinder volume is 2 times that of the volume of the cone