All GRE Math Resources
Example Question #11 : Spheres
If a sphere has a volume of cubic inches, what is the approximate radius of the sphere?
The formula for the volume of a sphere is
where is the radius of the sphere.
, giving us .
Example Question #12 : Spheres
A rectangular prism has the dimensions . What is the volume of the largest possible sphere that could fit within this solid?
For a sphere to fit into the rectangular prism, its dimensions are constrained by the prism's smallest side, which forms its diameter. Therefore, the largest sphere will have a diameter of , and a radius of .
The volume of a sphere is given as:
And thus the volume of the largest possible sphere to fit into this prism is
Example Question #13 : Spheres
What is the radius of a sphere with volume cubed units?
The volume of a sphere is represented by the equation . Set this equation equal to the volume given and solve for r:
Therefore, the radius of the sphere is 3.