Questions: 10. Water is filled in a cuboidal swimming pool at a rate of 1200 litres per minute. If the swimming pool is 18 m long, 12 m broad and 2 m deep, find the number of hours it will take to fill the pool.

Solution Steps

The volume \( V \) of a cuboidal swimming pool can be calculated using the formula:

\[ V = \text{length} \times \text{breadth} \times \text{depth} \]

Given:

• Length = 18 m
• Breadth = 12 m
• Depth = 2 m

Substituting these values into the formula:

\[ V = 18 \times 12 \times 2 = 432 \, \text{m}^3 \]

Since 1 cubic meter is equivalent to 1000 litres, we convert the volume from cubic meters to litres:

\[ V = 432 \, \text{m}^3 \times 1000 \, \text{litres/m}^3 = 432,000 \, \text{litres} \]

The pool is filled at a rate of 1200 litres per minute. To find the time \( t \) in minutes required to fill the pool, we use the formula:

\[ t = \frac{\text{Total Volume in Litres}}{\text{Filling Rate in Litres per Minute}} \]

Substituting the known values:

\[ t = \frac{432,000}{1200} = 360 \, \text{minutes} \]

To convert the time from minutes to hours, divide by 60:

\[ t = \frac{360}{60} = 6 \, \text{hours} \]

Final Answer