Question

Imagine you are comparing two cubes: one that is 30 kg and measures 3m on each side, and one that is 40 kg and measures 4m on each side.

-Which cube has a larger weight? Explain your reasoning

-Which cube has a larger volume? Explain your reasoning.

-Which cube has a larger density? Explain your reasoning.

Answer 1

Part A.

given that mass of cube 1: 30 kg, side of cube 1 = 3 m

mass of cube 2: 40 kg, side of cube 2 = 4 m

Weight is given by: Weight = mass*g

W1 = m1*g, where g = acceleration due to gravity = 10 m/s^2, So

W1 = 30*10 = 300 N

W2 = m2*g = 40*10 = 400 N,

So 2nd cube will have larger weight, because mass of 2nd cube is higher than mass of 1st cube

Part B.

Volume of cube is given by: V = side^3 = a^3

V1 = a1^3 = 3^3 = 27 m^3

V2 = a2^3 = 4^3 = 64 m^3

So 2nd cube will have larger Volume, because side of 2nd cube is higher than side of 1st cube

Part C.

Density is given by: density = Mass/Volume

$\rho$ = mass/Volume

$\rho$1 = m1/a1^3 = 30/3^3 = 1.11 kg/m^3

$\rho$2 = m2/a2^3 = 40/4^3 = 0.625 kg/m^3

So 1st cube will have larger density

Let me know if you've any query.