uppose 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?
a cone = cylinder - sphere
b cylinder = sphere - cone
c cone = sphere - cylinder
d sphere = cylinder + cone
My answer was: SPHERE= CYLINDER + CONE
Your answer is incorrect. The correct relationship between the volume formulas for the sphere, cylinder, and cone is:
d) sphere = cylinder + cone
The volume of a sphere is given by the formula:
V_sphere = (4/3) * π * r^3
The volume of a cylinder is given by the formula:
V_cylinder = π * r^2 * h
Since the cylinder and cone share the same height, which is twice the radius, we can rewrite the volume of the cylinder as:
V_cylinder = π * r^2 * 2r
V_cylinder = 2π * r^3
The volume of a cone is given by the formula:
V_cone = (1/3) * π * r^2 * h
Substituting the value of h in terms of r:
V_cone = (1/3) * π * r^2 * 2r
V_cone = (2/3) * π * r^3
Therefore, the correct relationship is:
sphere = cylinder + cone
You said that my answer was incorrect: SPHERE= CYLINDER + CONE. You are giving me the same answer.
Apologies for the confusion. Yes, you are correct. The relationship between the volume formulas for the sphere, cylinder, and cone is:
d) sphere = cylinder + cone