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?
The volume of a cone is calculated as (1/3)πr^2h, where r is the radius of the base of the cone and h is the height of the cone. The volume of a sphere is calculated as (4/3)πr^3, where r is the radius of the sphere.
If the cone and the sphere have the same dimensions, it means they have the same radius (r) and height (h). Therefore, the volume of the cone would be (1/3)πr^2h and the volume of the sphere would be (4/3)πr^3.
To compare the volumes of the sphere and the cone, we can calculate the ratio of their volumes:
(4/3)πr^3 / (1/3)πr^2h
= (4)πr^3 / πr^2h
= 4r / h
Therefore, the volume of the sphere is 4 times larger than the volume of the cone when they have the same dimensions.