Question

So the polynomial 24r squared represents the surface are of a cube a : determine the polynomial that represents the area of one face of the cube b: use this answer to determine a polynomial that represents the length of an edge of the cube c: what is the length of an edge of the cube when r = 3 cm

Answer 1

a. 4r² b. 2r c. 6 cm

Explanation:

The surface area A of the cube is A = 24r². We know that the surface area, A of a cube also equals A = 6L² where L is the length of its side.

Now, equating both expressions, 6L² = 24r²

dividing both sides by 6, we have

6L²/6 = 24r²/6

L² = 4r². Since the area of one face is L², the polynomial that determines the area of one face is A' = 4r².

b. Since L² = 4r² the rea of one face of the cube, taking square roots of both sides, we have

√L² = √4r²

L = 2r

So, the polynomial that represents the length of an edge of the cube is L = 2r

c. The length of an edge of the cube is L = 2r. When r = 3 cm.

L = 2r = 2 × 3 cm = 6 cm

So, the length of an edge of the cube is 6 cm.