Question

The surface area, (S), of a cube is directly proportional to the square of the length of its side. The mass, (M), of the cube is directly proportional to the cube of the length of its side. Work out an equation of proportionality that relates (S) to (M).

a) S = k/k' . 1/s
b) S = k ⋅ s²
c) S = k'/k . 1/s
d) S = k' ⋅ s³

Answer 1

The equation of proportionality that relates the surface area (S) of a cube to its mass (M) is S = (k' / k) * (1 / s).

Step-by-step explanation:

The equation of proportionality that relates the surface area (S) of a cube to its mass (M) can be found by considering the given information.

It is stated that the surface area of the cube is directly proportional to the square of the length of its side, so we can write this as:

S = k * s^2,

where S is the surface area, k is the constant of proportionality, and s is the length of the side of the cube.

It is also stated that the mass of the cube is directly proportional to the cube of the length of its side, so we can write this as:

M = k' * s^3,

where M is the mass and k' is the constant of proportionality.

Therefore, the equation of proportionality that relates S to M is:

S = k * (s^2) = k * [(s^3) / s] = (k' / k) * (s^3 / s) = (k' / k) * s^2/s = (k' / k) * (1 / s).