Answer:
h ≈ 77 cm
Step-by-step explanation:
Let us convert the liters to cm³.
Smaller barrel
0.001 litres = 1 cm³
100 litres = 100000 cm³
Larger barrel
0.001 litres = 1 cm³
160 litres = 160000 cm³
For a similar solid figure the cube of their corresponding sides is equal to the volume ratio.
This means
h³/90³ = 100000/160000
cube root both sides
h/90 = ∛100000 / ∛160000
h/90 = 46.4158883/54.2883523
cross multiply
54.2883523h = 46.4158883 × 90
54.2883523h = 4177.429947
divide both side by 54.2883523
h = 4177.429947/54.2883523
h = 76.9489175858
h ≈ 77 cm
