Question

A family pool holds \[10,000\] gallons of water. How many cubic metres is this?

Answer 1

Hint: These types of problems are pretty straight forward and are very simple to solve. To solve this type of given sums, we need to have a clear cut idea of units and measurements and the conversion from one unit to another efficiently. First of all there are different units for measuring one particular thing, for example, volume can be measured in terms of gallons, litres, cubic meters etc. So, we can understand from this that gallon is a unit of volume. Thus we first need to convert gallons to litres, then from litres to cubic centimeters and then to cubic metres to get our desired result.

Complete step-by-step solution:
Now we start off with the solution to our given problem by writing that, we first of need to remember a relation that would help us in solving the problem very easily and quickly. The conversion factor from gallons to litres is \[3.785\] , which means,
\[1\] gallon = \[3.785\] litre, Thus,
\[10,000\] gallons = \[37850\] litres.
Now, we convert litres to cubic centimeters by the relation,
\[1\] litres = \[1\] cubic decimetres.
Therefore, \[37850\] litres = \[37850\] cubic decimetres.
After this we need to convert cubic decimetres to cubic metres by a multiplying factor, we know,
\[1\] decimetre = \[\dfrac{1}{10}\] metre,
Therefore, \[1\] cubic decimetre = \[\dfrac{1}{1000}\] cubic metre
Thus converting the intermediate cubic decimetre to cubic metre, we get,
\[37850\] cubic decimetre = \[\dfrac{1}{1000}\times 37850\] cubic metre
\[37.850\] cubic metres.
Therefore, we get, \[10,000\] gallons = \[37.850\] cubic metres.

Note: For such a type of problem we need to be aware of the topic units and measurements and we must be able to comfortably switch from one unit to another by means of various relations. We must also be very careful when we convert from one unit to another, especially from CGS system to SI system. The relations from one unit to another should be defined properly for convenient use.