A cubical water tank is 1.2 m high. How many litres of water does it hold? ($1000 cm^3 = 1$ litre)
Answer (2)
Convert the height of the tank from meters to centimeters: 1.2 m = 120 c m .
Calculate the volume of the tank in cubic centimeters: V o l u m e = ( 120 c m ) 3 = 1728000 c m 3 .
Convert the volume from cubic centimeters to litres: V o l u m e = 1728000 c m 3 = 1728 l i t res .
The cubical water tank holds 1728 litres of water.
Explanation
Problem Analysis The problem states that a cubical water tank is 1.2 m high and asks for the volume of water it can hold in litres, given that 1000 c m 3 = 1 litre.
Convert meters to centimeters First, we need to convert the height of the tank from meters to centimeters. Since 1 meter is equal to 100 centimeters, we have: 1.2 m = 1.2 m × 1 m 100 c m = 120 c m
Calculate volume in cubic centimeters Since the tank is cubical, all its sides are equal. Therefore, the volume of the tank in cubic centimeters is: V o l u m e = ( s i d e ) 3 = ( 120 c m ) 3 = 120 c m × 120 c m × 120 c m = 1728000 c m 3
Convert cubic centimeters to litres Now, we need to convert the volume from cubic centimeters to litres. We are given that 1000 c m 3 = 1 l i t re . Therefore: V o l u m e = 1728000 c m 3 = 1728000 c m 3 × 1000 c m 3 1 l i t re = 1728 l i t res
Final Answer Therefore, the cubical water tank holds 1728 litres of water.
Examples
Understanding volume calculations is crucial in many real-life scenarios. For instance, when planning a fish tank, knowing how to calculate the volume helps determine the amount of water needed and the number of fish the tank can comfortably accommodate. Similarly, in construction, calculating the volume of concrete needed for a foundation ensures accurate material ordering and cost estimation. These calculations also play a vital role in fields like medicine, where precise dosages are essential, and in environmental science, where monitoring water levels in reservoirs is critical for water resource management. The ability to accurately calculate volumes ensures efficiency, safety, and sustainability in various practical applications.
The cubical water tank holds 1728 litres of water. This is calculated by first converting the height to centimeters, then finding the volume in cubic centimeters, and finally converting that volume to litres. The final result is 1728 litres.
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