Question

The mass of a cube, M (kg), is proportional to the cube of the length of its edge, L(m). The mass of the cube is 80 kg when the length of its edge is 35 cm. Work out M (to 2 DP) when L=0.3 m

Answer 1

M=K*L

(K is the constant we use)

when L=35cm, M=80,

meaning K=80/0.35=228.571428571

so when L=0.3

we do 0.3*228.571428571=68.5714285713

rounded to 2dp= 68.57kg

Answer 2

9514 1404 393

Answer:

50.38 kg

Explanation:

The mass is proportional to the cube of edge length, So, if the edge length is decreased by a factor of 30/35 = 6/7, the mass is decreased by a factor of (6/7)³. That is, the smaller cube will have a mass of ...

(80 kg)(6/7)³ ≈ 50.38 kg

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If you want to write an equation, you can write the equation for the proportionality:

M = kL³

80 kg = k(0.35 m)³

k = 80/0.35³ kg/m³

Then for the shorter length, we have ...

M = k(0.3 m)³ = 80(0.3/0.35)³ kg = 80(6/7)³ kg ≈ 50.38 kg . . . . as above