a sphere with a diameter 6 inches is inscribed in a cube. WHat is the volume of the space between the sphere and the cube?
Accepted Solution
A:
Answer:[tex]102.9in^{3}[/tex]Step-by-step explanation:In order to calculate the space between the sphere and the cube we need to calculate the volume of the cube and then the volume of the sphere. I have attached an illustration below to help you better understand the situation.[tex]Volume.Cube = a^{3}[/tex][tex]Volume.Sphere = \frac{4}{3}*\pi *r^{3}[/tex] .... r is radius which is half of diameter.Now that we know the formulas we can solve for the volumes.[tex]Volume.Cube = 6^{3}[/tex][tex]Volume.Cube = 216.in^{3}[/tex][tex]Volume.Sphere = \frac{4}{3}*\pi *r^{3}[/tex][tex]Volume.Sphere = 113.097in^{3}[/tex]Now we can subtract the volume of the sphere from the volume of the cube in order to calculate the space between them[tex]216-113.1 = 102.9in^{3}[/tex]The space between is that of [tex]102.9in^{3}[/tex]