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 100 kg when
the length of its edge is 20 cm.
Work out L (to 2 DP) when M = 1900
kg

Thanks

Answer 1

380.00

Explanation:

M=KL

100=20K

K=5

M=5L

1900=5L

L=380

Answer 2

L = 53.37 cm

Explanation:

We have the relationship

M ∝ L³

We can rewrite this as an equation:
M = k · L³

where k, a constant, is known as the constant of proportionality

Given M = 100 kg when L = 20, we get

100 = k · 20³

100 = k · 8000

k = 100/8000 = 0.0125

If M = 1900 kg and k = 0.0125 we can plug in these values to get

1900 = 0.0125 L³

==> L³ = 1900/0.0125

==> L³ = 152000

Therefore L = ∛152000

L = 53.36803 or

L = 53.37 cm rounded to 2 DP