Assume a cube has side lengths of 2 inches. What is the area of the base of that cube? Does it matter which face we call the base? What is the volume of that cube? Instead, assume the cube has side lengths of 3 inches. What is the area of the base now? The volume? Based on that, what do you think the relationship is between side length, area, and volume? Would that still be true even if it is not a cube? (Put another way, if the side length is x, what is the area and volume?)

Step-by-step explanation:

Volume of a cube:

V = a3

Surface area of a cube:

the area of each face (a x a) times 6 faces

S = 6a2

Face diagonal of a cube:

By the pythagorean theorem we know that

f2 = a2 + a2

Then f2 = 2a2

solving for f we get

f = a√2

Diagonal of the solid cube:

Again, by the pythagorean theorem we know that

d2 = a2 + f2

substituting f into this equation we get

d2 = a2 + (a√2)2 = a2 + 2a2 = 3a2

solving for d we get

d = a√3

answer: entity is prob the answer

step-by-step explanation: