Suppose a sphere, cylinder, and cone all share the same radius. The cylinder and cone also share the same height, which is twice the radius. Which of the following is true about the relationship between the volume formulas for the sphere, cylinder, and cone?(1 point)
The volume formula for a sphere is 4/3πr^3.
The volume formula for a cylinder is πr^2h.
The volume formula for a cone is 1/3πr^2h.
Since the radius is the same for all three shapes, we can compare the volume formulas based on the respective height.
The height of the cylinder and cone is twice the radius, so we can substitute 2r for h in the formulas.
The volume of the sphere remains the same as the formula does not involve the height.
Comparing the volume formulas for the cylinder and cone:
- The volume of the cylinder is πr^2(2r) = 2πr^3.
- The volume of the cone is 1/3πr^2(2r) = 2/3πr^3.
Therefore, the volume formula for the cylinder is twice as large as the volume formula for the cone.
To summarize, the relationship between the volume formulas for the sphere, cylinder, and cone is:
Sphere volume = Cylinder volume
Cylinder volume = 2 x Cone volume