Question

The dimensions of the tank are 50 cm by 32 cm by 20 cm. The tank is full of water and sand. The ratio of the volume of water to the volume of sand is 5 : 1 Work out the number of litres of water in the tank.

Answer 1

Given:

Dimensions of a tank are 50 cm by 32 cm by 20 cm

The tank is full of water and sand

Ratio of volume of water to the volume of sand is 5:1

To find:

Volume of water in the tank in liters

Solution:

Without loss of generality, let,

Length of tank = 50 cm

Breadth of tank = 32 cm

Height of tank = 20 cm

Then, we have,

Total Volume of the tank = Length * Breadth * Height

$\Rightarrow$ Total Volume = 50*32*20 cc

$\Rightarrow$ Total Volume = 32000 cc

It is given that,

Volume of water : Volume of sand = 5:1

$\Rightarrow$ (Volume of water)/(Volume of sand) = 5/1

Cross multiplying, we have,

Volume of sand = (Volume of water)/5

It is also given that the tank is full of water and sand. This implies that,

Volume of water + Volume of sand = Total Volume

Using the value, we obtained, we get,

Volume of water + (Volume of water)/5 = Total Volume

$\Rightarrow$ (6 * Volume of water)/5 = Total Volume

Plugging in the value of total volume, we get,

$\Rightarrow$ (6 * Volume of water)/5 = 32000 cc

$\Rightarrow$ Volume of water = $\frac{32000*5}{6}$ cc

$\Rightarrow$ Volume of water $\approx$ 26,666.6667 cc

We know that,

1 cc = 0.001 liters

$\Rightarrow$ 26,666.6667 cc = (26666.6667 * 0.001) liters

$\Rightarrow$ 26,666.6667 cc $\approx$ 26.667 liters

Thus, Volume of water in the tank is approximately 26.667 liters

Final Answer:

Volume of water in the tank (in liters) is approximately 26.667 liters