Question
Suppose a cylinder and a cone share the same radius and the same height, which is twice the radius. Which ratio describes the relationship between the formulas for the volume of a consta
Answers
GPT 3.5
The volume V of a cylinder is given by the formula Vc = πr^2h, where r is the radius and h is the height.
The volume V of a cone is given by the formula Vc = (1/3)πr^2h, where r is the radius and h is the height.
In this case, the height of the cylinder is twice the radius, so h = 2r.
Plugging this value into the volume formulas, we get:
Vcylinder = πr^2(2r) = 2πr^3
Vcone = (1/3)πr^2(2r) = (2/3)πr^3
The ratio between the formulas for the volume of a cylinder and a cone with the same radius and height is:
Vcylinder/Vcone = (2πr^3)/[(2/3)πr^3] = 3/2
So, the ratio describing the relationship between the formulas for the volume of a cylinder and a cone with the same radius and height is 3/2.
The volume V of a cone is given by the formula Vc = (1/3)πr^2h, where r is the radius and h is the height.
In this case, the height of the cylinder is twice the radius, so h = 2r.
Plugging this value into the volume formulas, we get:
Vcylinder = πr^2(2r) = 2πr^3
Vcone = (1/3)πr^2(2r) = (2/3)πr^3
The ratio between the formulas for the volume of a cylinder and a cone with the same radius and height is:
Vcylinder/Vcone = (2πr^3)/[(2/3)πr^3] = 3/2
So, the ratio describing the relationship between the formulas for the volume of a cylinder and a cone with the same radius and height is 3/2.