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Two barrels are mathematically similar
The smaller barrel has a height of [tex]h[/tex]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 [tex]h[/tex]

Two barrels are mathematically similar The smaller barrel has a height of texhtexcm and a capacity of 100 Liters The larger barrel has a height of 90cm and a ca class=

Respuesta :

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

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