A rectangular tank 60 cm long and 50 cm wide is /5 full of water. When 24 liters of water are added, the water level rises to the brim of the tank. Find the height of the tank. (1 liter is 1000cm3 )

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Answer:

The tank is 10cm high

Step-by-step explanation:

Given

[tex]L=60cm[/tex] — length

[tex]W=60cm[/tex] — width

[tex]x = \frac{1}{5}[/tex] — water lever

[tex]Addition = 24L[/tex]

Required

The height of the tank

Let y represents the remaining fraction before water is added.

Answer:The tank is 10cm high

Step-by-step explanation:Given[tex]L=60cm[/tex]

— length[tex]W=60cm[/tex]

— width[tex]x = \frac{1}{5}[/tex]

— water lever[tex]Addition = 24L[/tex]

RequiredThe height of the tank

Let y represents the remaining fraction before water is added.So:[tex]y + x = 1[/tex]

Make y the subject[tex]y = 1 – x[/tex]

[tex]y = 1 – \frac{1}{5}[/tex]

Solve[tex]y = \frac{5 – 1}{5}[/tex]

[tex]y = \frac{4}{5}[/tex]

Represent the volume of the tank with vSo:[tex]y * v = 24L[/tex]

Make v the subject[tex]v = \frac{24L}{y}[/tex]

Substitute:[tex]y = \frac{4}{5}[/tex][tex]v = \frac{24L}{4/5}[/tex]

[tex]v = 30L[/tex]

Represent the height of the tank with h;So, the volume of the tank is:[tex]v = lwh[/tex]

Make h the subject[tex]h = \frac{v}{lw}[/tex]

Substitute values for v, l and w[tex]h = \frac{30L}{60cm * 50cm}[/tex]

Convert 30L to cm^3[tex]h = \frac{30*1000cm^3}{60cm * 50cm}[/tex]

[tex]h = \frac{30000cm^3}{3000cm^2}[/tex]

[tex]h = 10cm[/tex]