Question

what is the volume of the largest possible cube cut out of a solid sphere of volume 36pie cm3

Answer 1

Answer:

Step-by-step explanation:

The Volume of Solid Sphere = 4/3πr³ = 36π

=> r³ = 36π * 3/4π = 27

=> r = 3 cm.

radius of sphere = 3 cm.

Diameter of Sphere = 6 cm.

The largest cube that can be enclosed within a sphere will have its diagonal equal to diameter of sphere.

=> Diagonal of cube = diameter of sphere

Formula for Diagonal of cube = √3a

=> √3a =  6

=> a = 6/√3 = 6√3/3 = 2√3 cm.

Now volume of cube = a³ = (2√3)³ = (2)³ * (√3)³ = 8 * 3√3 = 24√3 cm³.