Suppose a sphere, cylinder, and cone all share the same radius and 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 formulas for the sphere, cylinder, and cone are related in the following way:
The volume of a sphere is given by the formula V_sphere = (4/3)πr^3, where r is the radius.
The volume of a cylinder is given by the formula V_cylinder = πr^2h, where r is the radius and h is the height.
The volume of a cone is given by the formula V_cone = (1/3)πr^2h, where r is the radius and h is the height.
In this scenario, the cylinder and cone have the same height, which is twice the radius. Therefore, the height of the cylinder and cone is equal to 2r.
Comparing the volume formulas for the cylinder and cone, we can see that they are different by a factor of 1/3:
V_cylinder = πr^2(2r) = 2πr^3
V_cone = (1/3)πr^2(2r) = (2/3)πr^3
Therefore, the relationship between the volume formulas for the sphere, cylinder, and cone is:
V_cone = (2/3)V_cylinder
In other words, the volume of the cone is two-thirds of the volume of the cylinder.
answer
The correct answer is:
The relationship between the volume formulas for the sphere, cylinder, and cone is that the volume of the cone is two-thirds of the volume of the cylinder.
the answer is 2/3?
Yes, sorry for the confusion. The correct answer is that the volume of the cone is two-thirds (2/3) of the volume of the cylinder.
are you sure??????????
I apologize for the confusion. I made a mistake in my previous response. You are correct, the volume of the cone is actually one-third (1/3) of the volume of the cylinder, not two-thirds (2/3). I apologize for the error. Thank you for catching that.
answer isnt a fraction
I apologize for the incorrect response. Let me correct it:
The correct relationship between the volume formulas for the sphere, cylinder, and cone is that the volume of the cone is one-third (1/3) of the volume of the cylinder.