Here are two cubes, A and B. Cube A has a mass of 81 g. Cube B has a mass of 128 g. __ Work out the density of cube A : the density of cubc B Give your answer in the form a:b where a and b are integers.

## Step 1: First, we need to find the volume of each cube. The volume of a cube is given by the formula , where is the length of one side. However, in this problem, we are not given the side lengths of the cubes. Instead, we are given their masses and asked to find their densities. ## Step 2: The density of an object is defined as its mass divided by its volume. The formula for density is , where is the density, is the mass, and is the volume. ## Step 3: We are given the masses of the cubes, but not their volumes. However, since the cubes are identical in size, we can say that their volumes are equal. Therefore, the ratio of their densities will be the same as the ratio of their masses. ## Step 4: The ratio of the densities of the two cubes is therefore , where and are the densities of cubes A and B, and and are their respective masses. ## Step 5: Substitute the given values into the formula. We have and . Therefore, . ## Step 6: To simplify the ratio, we divide both numbers by their greatest common divisor (GCD). The GCD of 81 and 128 is 1. Therefore, the simplified ratio is .