What is the answer for # 24?

a b c or d

The volume of the space not filled by the sphere is the difference between the volume of a cube with edge length 6 inches and the volume of a sphere with radius 3 inches.

The volume of a cube of edge length s is

... V = s³

When the edge length is 6 in, the volume is

... V = (6 in)³ = 216 in³

The volume of a sphere with radius r is

... V = (4/3)π·r³

When the radius is 3 in, the volume is

... V = (4/3)π·(3 in)³ = 36π in³

Then the volume of the space between the cube and the sphere is

... Vcube - Vsphere = 216 in³ - 36π in³ ≈ 102.9 in³ . . . . corresponding to choice C

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b