The volume of the cone is 25π.
(5 points)
The volume of the sphere if the radius is the same value as the cone.
The volume of the cylinder
How many times larger is the volume of the sphere than the volume of the cone IF the cone and the sphere had the same dimensions?
In order for the volume of the cone + the volume of the sphere = the volume of the cylinder, the height would have to be _______, not 3r for the cone and cylinder.
How many times larger is the volume of the cylinder than the volume of the cone IF the cone and the cylinder had the same dimensions?
Volume of the cone = 1/3πr^2h = 25π
Given that the radius of the cone is equal to the radius of the sphere, we can say that r=h
Therefore, 1/3πr^3 = 25π
r^3 = 75
r = h = (75)^(1/3)
Volume of the sphere = 4/3πr^3 = 4/3π(75)^(1/3)^3 = 100π
Volume of the cylinder = πr^2h = π(75)^(1/3)^2 * (75)^(1/3) = 75π
The volume of the sphere is 100π/25π = 4 times larger than the volume of the cone if they had the same dimensions.
To make the volume of the cone + volume of the sphere = the volume of the cylinder, the height would have to be 2(75)^(1/3), rather than 3r for the cone and cylinder.
The volume of the cylinder is 75π/25π = 3 times larger than the volume of the cone if they had the same dimensions.