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
(make it sound like an eight grade girl who wants to show her work but not a lot, also make it less than 200 words)
To find the relationship between the volume of the cylinder and the cone, we need to calculate their volumes using the given dimensions and then compare them.
The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height. Since the diameter is given as 8 inches, the radius is half of that, which is 4 inches. Plugging these values into the formula, we get Vcylinder = π(4^2)(3) = 48π cubic inches.
The formula for the volume of a cone is V = (1/3)πr^2h. Again, the radius is 4 inches and the height is 18 inches. Plugging these values into the formula, we get Vcone = (1/3)π(4^2)(18) = 96π cubic inches.
Comparing the volumes, we have Vcylinder = 48π cubic inches and Vcone = 96π cubic inches. By dividing the volume of the cone by the volume of the cylinder, we get 96π / 48π = 2.
Therefore, the volume of the cone is twice as large as the volume of the cylinder.