A sphere of radius r is packed in a box of cubical shape. What should be the minimum volume (in cm^3) of the box that ca...

Question

A sphere of radius r is packed in a box of cubical shape. What should be the minimum volume (in cm^3) of the box that can enclose the sphere?

A. (4/3)*pi*r^3
B. pi*r^3
C. 8*r^3
D. 8*pi*r^3

Accepted Answer

Minimum volume of the cubical box = 8*r^3. A sphere of radius r just fits inside a cube when the cube's side equals the diameter of the sphere (2r). The minimum box that can enclose the sphere is a cube whose side length equals the diameter of the sphere. The volume of such a cube is (2r)^3.

A sphere of radius r is packed in a box of cubical shape. What should be the minimum volume (in cm^3) of the box that can enclose the sphere? A. (4/3)*pi*r^3 B. pi*r^3 C. 8*r^3 D. 8*pi*r^3

A sphere of radius r is packed in a box of cubical shape. What should be the minimum volume (in cm^3) of the box that can enclose the sphere? A. (4/3)pir^3 B. pir^3 C. 8r^3 D. 8pir^3