Question

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 )

Answer 1

Answer:

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

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

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

$h = 10cm$