Question

An empty tank was $\dfrac{2}{5}$ full after 1.5 liters of water was poured into it. The base area of the tank was $250\;c{m^2}$. What was the height of the tank?

Answer 1

Hint: This is a problem of mensuration and requires the concept of volumes of 3-D objects. We will also require the conversion of liters into square centimeters. The general form of the volume of any 3-D object is given by-
${\text{V}} = {\text{A}} \times {\text{h}}, \text{where A is the area of base and h is the height} $...........(1)

Complete step-by-step solution -
We have been given that the tank is two-fifth full when 1.5 litres of water is poured. This means that 1.5 litres is the two-fifths of the total volume of the tank. Let the volume of the tank be V. Mathematically-
$\dfrac{2}{5} \times {\text{V}} = 1.5$
${\text{V}} = 1.5 \times \dfrac{5}{2} = 3.75\;litres$
We have been given the base area of the tank. We also know that-
$1\;litre\; = \;1\;d{m^3}\;so,\;$
$1\;litre\; = \;\left( {10 \times 10 \times 10} \right)c{m^3}$
$1\;litre\; = \;1000\;c{m^3}$
So, we can write the value of V as-
${\text{V}} = 3.75\;litres$
${\text{V}} = 3.75 \times 1000\;c{m^3}$
${\text{V}} = 3750\;c{m^3}$
Now, to find the height of the tank, we will apply formula (1) as-
${\text{V}} = {\text{A}} \times {\text{h}}$
$3750 = 250{\text{h}}$
${\text{h}} = \dfrac{{3750}}{{250}} = 15\;cm$
This is the required height of the tank.

Note: The students often become confused in such questions because the type of the container is not given, that is, cylindrical, cuboidal, cubic, and so on. But here, we do not require the type of container because we can apply the general formula for volume which is the area of base times the height. Also, we should remember the formula of conversion of units of volume, and never forget to write the units in the final answer.