The edge of a wooden cube is 10 cm. It was covered with plasticine from above so that the edge became 12 cm

The edge of a wooden cube is 10 cm. It was covered with plasticine from above so that the edge became 12 cm. Determine the mass of the plasticine if its density is 1720 kg / m³

Let the length of the edge of the wooden cube be equal to a, and the length of the edge covered with plasticine equal to b

Then the volume of the original wooden cube is equal to Vder = a³, and the total volume of the plasticine covered with V = b³

In this case, the volume of only plasticine from the entire volume will be

Vplast = V – Vder = b³ – a³

Knowing the density of plasticine and its volume, it is not difficult to calculate the mass:

m = pV = p * (b³ – a³)

Numerically:

p = 1720 [kg / m³] = 1.72 [g / cm³]

m = 1.72 [g / cm³] * ((12 [cm]) ³ – (10 [cm]) ³) = 1.72 * (12³ – 10³) [g] = 1.72 * (1728 – 1000 ) [g] = 1252 [g] = 1.25 [kg]

Answer: the mass of plasticine is 1.25 kg