Question

3. Two solid cubes have same mass but their Surface areas are in the ratio of the 1:16 what is the ratio of their densities​

Answer 1

Answer:

Explanation:

Let's assume that the two solid cubes have masses m each and surface areas S1 and S2 respectively. We are given that the ratio of the surface areas is 1:16, so we can write:

S2/S1 = 16/1

S2 = 16S1

We also know that the density of an object is given by its mass divided by its volume, or:

density = mass/volume

The volume of a cube is given by the formula:

volume = side^3

Since the two cubes have the same mass, their densities are proportional to their volumes. Let's call the side length of the first cube x, so its volume is x^3. The side length of the second cube must be 2x (since its surface area is 16 times larger), so its volume is (2x)^3 = 8x^3. Therefore, the ratio of their volumes is:

V2/V1 = 8x^3 / x^3 = 8

Now we can write the ratio of their densities as:

density2/density1 = (mass/V2) / (mass/V1) = V1/V2

Substituting the expressions we have found for V2/V1 and S2/S1, we get:

density2/density1 = 1/8

Therefore, the ratio of the densities of the two cubes is 1:8.