Ahollow sphere sits snugly in a foam cube so that the sphere touches each side of the cube. find the volume of the foam.

                             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

false

step-by-step explanation:

4y - 6 + 4y^2 - 9

before simplifying this contains 4 terms

after simplifying

4y -15 + 4y^2

it contains 3 terms

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!