The side of a cube is represented by x feet. Polynomial

Question

The side of a cube is represented by x feet. A. Write a polynomial that represents the volume of a cube. B. Write a polynomial that represents the surface area of a cube. C. You increase each side of the cube by 1 foot. Write a polynomial that represents the new volume of the cube. D. You double the length of each side of the cube by 1 foot. Write a polynomial that represents the new surface area of the cube.

Answer 1

A cube has all six sides congruent.

Each side is a square with x feet along each edge.

A) V = L · W · H = x · x · x =x³ So V = x³

B) Area of each square surface is L ·W = x · x = x² and there are 6 surfaces (front, back, top, bottom, left, right), so SA = 6x²

C) Each side now is x+1, so the new volume is given by V_new = (x+1)³

D) Double each side, now each side is 2x. The area of each surface is (2x)² = 4x² and there are 6 surfaces, so the new surface area is 6 · 4x² and is given by SA_new = 24x²

Answer 2

volume = x^3

surface area = 6*x^2

sides increase by 1:

volume = (x+1)^3

surface area = 6(x+1)^2

doubles the side:

volume = (2x)^3

surface area = 6 ( 2x)^2

double and add one:

volume = (2x+1)^3

surface area = 6(2x+1)^2