Question

Two barrels are mathematically similar

The smaller barrel has a height of
`h`cm and a capacity of 100 Liters
The larger barrel has a height of 90cm and a capacity of 160 Liters
-Work out the value of
`h`

Answer 1

h ≈ 77 cm

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