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.
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.
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.
Answers
Answered by
GPT 3.5
To determine the relationship between the volume of the cylinder and the cone, we need to calculate their volumes and compare them.
The volume of a cylinder can be calculated using the formula: Vcylinder = πr^2h, where r is the radius (half the diameter) and h is the height.
Given that the diameter of both the cylinder and the cone is 8 inches, the radius (r) of both the shapes would be 8/2 = 4 inches.
The height of the cylinder is given as 3 inches, so we have:
Vcylinder = π(4^2)(3) = 48π cubic inches
The volume of a cone can be calculated using the formula: Vcone = (1/3)πr^2h.
Given that the diameter of the cone is also 8 inches, the radius (r) would be 4 inches.
The height of the cone is given as 18 inches, so we have:
Vcone = (1/3)π(4^2)(18) = 96π cubic inches.
Comparing the volumes of the cylinder and the cone, we have:
Vcylinder = 48π cubic inches
Vcone = 96π cubic inches
The relationship between these two volumes is that the volume of the cone is twice the volume of the cylinder. In other words, the volume of the cone is doubled compared to the volume of the cylinder with the same diameter.
The volume of a cylinder can be calculated using the formula: Vcylinder = πr^2h, where r is the radius (half the diameter) and h is the height.
Given that the diameter of both the cylinder and the cone is 8 inches, the radius (r) of both the shapes would be 8/2 = 4 inches.
The height of the cylinder is given as 3 inches, so we have:
Vcylinder = π(4^2)(3) = 48π cubic inches
The volume of a cone can be calculated using the formula: Vcone = (1/3)πr^2h.
Given that the diameter of the cone is also 8 inches, the radius (r) would be 4 inches.
The height of the cone is given as 18 inches, so we have:
Vcone = (1/3)π(4^2)(18) = 96π cubic inches.
Comparing the volumes of the cylinder and the cone, we have:
Vcylinder = 48π cubic inches
Vcone = 96π cubic inches
The relationship between these two volumes is that the volume of the cone is twice the volume of the cylinder. In other words, the volume of the cone is doubled compared to the volume of the cylinder with the same diameter.
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