# 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 th

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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1. thanhha

The tank is 10cm high

Step-by-step explanation:

Given

$$L=60cm$$ — length

$$W=60cm$$ — width

$$x = \frac{1}{5}$$ — water lever

$$Addition = 24L$$

Required

The height of the tank

Let y represents the remaining fraction before water is added.

So:

$$y + x = 1$$

Make y the subject

$$y = 1 – x$$

$$y = 1 – \frac{1}{5}$$

Solve

$$y = \frac{5 – 1}{5}$$

$$y = \frac{4}{5}$$

Represent the volume of the tank with v

So:

$$y * v = 24L$$

Make v the subject

$$v = \frac{24L}{y}$$

Substitute: $$y = \frac{4}{5}$$

$$v = \frac{24L}{4/5}$$

$$v = 30L$$

Represent the height of the tank with h;

So, the volume of the tank is:

$$v = lwh$$

Make h the subject

$$h = \frac{v}{lw}$$

Substitute values for v, l and w

$$h = \frac{30L}{60cm * 50cm}$$

Convert 30L to cm^3

$$h = \frac{30*1000cm^3}{60cm * 50cm}$$

$$h = \frac{30000cm^3}{3000cm^2}$$

$$h = 10cm$$