Question

A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 5 inches. The height of the cone is 15 inches. Use n = 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

Explanation:

The volume of a cylinder can be calculated using the formula: V_cylinder = π * r^2 * h_cylinder, where r is the radius and h_cylinder is the height of the cylinder.

Given that the diameter of both the cylinder and the cone is 8 inches, we can calculate the radius of the cylinder:

radius = diameter / 2 = 8 inches / 2 = 4 inches.

Plugging in the values, we get:

V_cylinder = 3.14 * (4 inches)^2 * 5 inches

= 3.14 * 16 square inches * 5 inches

= 3.14 * 80 cubic inches

= 251.2 cubic inches (approx.)

Now let's calculate the volume of the cone. The formula for the volume of a cone is: V_cone = (1/3) * π * r^2 * h_cone, where r is the radius and h_cone is the height of the cone.

Using the same radius as before (4 inches) and the given cone height of 15 inches, we can calculate:

V_cone = (1/3) * 3.14 * (4 inches)^2 * 15 inches

= (1/3) * 3.14 * 16 square inches * 15 inches

= (1/3) * 3.14 * 240 cubic inches

= 251.2 cubic inches (approx.)