Cube increase by a factor of 3/2, the side of original cube 5 cm
Answers (2)
Given a line of length S, the square is S^2 and the cube is S^3.
Your question is ambiguous because "cube" means both the side and the volume of the figure. But whatever you meant, the above relationships remain valid.
If the side increases by 3/2, the square increases by 9/4 and the volume increases by 27/16.
The edge of the original cube has length 5 cm.
The area A0 of one square side s0 of this cube is then
A0 = 5^2 cm^2.
1) If the edges of the cube are increased by a factor of 3/2, the area A1 is
A1 = (5 * 3/2)^2 = 5^2 * 9/4.
2) If the volume of the original cube is increased by 3/2, the edge S2 of the cube is:
S2 = (5^3 * 3/2)^(1/3) = 5 * (3/2)^(1/3) , and the area of one side A2 is
A2 = 5^2 * (3/2)^(2/3).
In case 1) the surface of cube 1 is then (6*A1) / (6*A0) times larger than the original cube. You see that the 6 (a cube has six sides) and the 5^2 cancel out, so the increased cube's surface is (3/2)^2 = 9/4 = 2.25 times larger than that of the original.
In case 2) you now see immediately that the surface area of the increased cube is
(3/2)^(2/3) = 1.31... times larger than that of the original cube.