Each face of a small cube has a surface area of 0.25 square meters. A larger cube has edges that are six times as long as the edges of the small cube. What is the volume of the larger cube?

Question

1.50 m3
3.375 m3
9 m3
27 m3

Answer 1

The surface area of one face of the small cube is 0.25 square meters. Since the cube has 6 faces, the total surface area of the small cube is 6 * 0.25 = 1.5 square meters.

Since the edges of the larger cube are six times as long as the edges of the small cube, the ratio of the volumes of the two cubes is 6^3 = 216.

If the volume of the small cube is x, then the volume of the larger cube is 216x.

We know that the surface area of the small cube is 1.5 square meters. The surface area of the larger cube is 6 * (6x)^2 = 36 * x^2.

Setting up an equation, we get:

36 * x^2 = 1.5

x^2 = 1.5 / 36

x^2 = 0.0416666667

x = sqrt(0.0416666667)

x = 0.204124145

Therefore, the volume of the larger cube is 216 * 0.204124145^3 ≈ 3.375 m3.

So, the correct answer is 3.375 m3.