Answer:
Explanation:
Let's assume that the diameter and height of the sphere and cylinder are both equal to "d" units, and the diameter and half-height of each cone are also equal to "d" units.
The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius. Since the diameter of the sphere is "d," the radius is d/2, so we can simplify the formula to V_sphere = (4/3)π(d/2)^3.
The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height. Since the diameter and height of the cylinder are both "d," the radius is also d/2, so we can simplify the formula to V_cylinder = π(d/2)^2d.
The formula for the volume of a cone is V = (1/3)πr^2h. Since the diameter and half-height of each cone are both "d," the radius is d/2, and the height is d/2. So we can simplify the formula to V_cone = (1/3)π(d/2)^2(d/2).
Now, let's compare the volumes of these shapes.
V_sphere/V_cylinder = [(4/3)π(d/2)^3]/[π(d/2)^2d] = (4/3)(d/2)/(d/2) = 4/3
V_cone/V_sphere = [(1/3)π(d/2)^2(d/2)]/[(4/3)π(d/2)^3] = (1/3)/(4/3)(d/2) = 1/4
Therefore, the ratio of the volume of the sphere to the volume of the cylinder is 4/3, and the ratio of the volume of the cone to the volume of the sphere is 1/4.
In other words, the volume of the sphere is 4/3 times the volume of the cylinder, and the volume of the cone is 1/4 times the volume of the sphere.