Question

A hollow sphere sits snugly in a foam cube so that the sphere touches each side of the cube. Find the volume of the foam.

Answer 1

Answer:

                             π

V-foam = 4r³( 2 - ----- )

                             3

Step-by-step explanation:

Let the radius of the sphere be r.  Then the volume of the sphere is

V = (4/3)(π)(r³).  

Next, recognize that the side length of the cube is 2r, and that the volume of the cube is thus

V = (2r)³, or 8r³.

Then the volume of the foam is equal to the volume of the cube less the volume of the sphere:

V-foam = 8r³ - (4/3)(π)(r³).  This could be factored into

                             π

V-foam = 4r³( 2 - ----- )

                             3

Answer 2

The volume of the foam is  : 8$r^{3}$

What is a cube?

A cube is a three dimensional shape made of 6 squares.

it has 8 corners and 12 edges.

Analysis:

Given that the sphere fits snugly in the cube the length of each face of the cube would be twice the radius of the sphere.

therefore:

L = 2r

where r = radius of sphere,

L = length of each face of cubic foam

volume of cubic foam = $L^{3}$

= $(2r)^{3}$

= $8r^{3}$

In conclusion, the volume of the cubic foam is  $8r^{3}$

learn more about three-dimensional shapes : brainly.com/question/11267313

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