During a uniform rain shower, 5 cm of rain falls on level ground. What is the total volume of water, in cubic metres, that falls on a field of area 1.5 hectares?

Introduction / Context:
This question links basic geometry with units used in real-life measurement of rainfall. When a certain depth of rain falls uniformly over a region, the total volume of water can be found by multiplying the area of the region by the rainfall depth, provided both are expressed in consistent units. The problem tests familiarity with hectares, conversion between centimetres and metres, and the simple formula for volume involving area and height (or depth).

Given Data / Assumptions:

• Rainfall depth = 5 cm.
• Area of the field = 1.5 hectares.
• 1 hectare = 10,000 square metres.
• We assume the rain falls uniformly over the entire area.
• We must express the final answer in cubic metres.

Concept / Approach:
Volume is given by:
Volume = Area * Depth To use this formula correctly, both area and depth must be in compatible units (for example, square metres and metres). Therefore, we convert hectares to square metres and centimetres to metres. Then we multiply the area by the converted depth to obtain the volume in cubic metres.

Step-by-Step Solution:
Convert area: 1 hectare = 10000 m^2, so 1.5 hectares = 1.5 * 10000 = 15000 m^2. Convert depth: 5 cm = 5 / 100 = 0.05 m. Use Volume = Area * Depth. Volume = 15000 m^2 * 0.05 m. Volume = 750 m^3.

Verification / Alternative check:
We can estimate to check reasonableness. A depth of 0.05 m is quite small compared to 1 m, and the area is 15000 m^2. If a depth of 1 m fell, the volume would be 15000 m^3. Because the actual depth is 1/20 of a metre, the volume should be roughly 15000 / 20 = 750 m^3. This confirms the exact calculation.

Why Other Options Are Wrong:
75 m^3 is ten times too small and would correspond to incorrectly using 0.005 m as the depth. 7500 m^3 and 75000 m^3 are too large and would result from misusing the area or depth conversion. 500 m^3 is also not consistent with the proportional reasoning above and would correspond to an incorrect intermediate step in the calculation.

Common Pitfalls:
Students often forget to convert centimetres to metres and directly multiply by 5 instead of 0.05. Some also confuse hectares with square kilometres or square metres, leading to major errors. Another common mistake is to convert the area correctly but still report the final answer in cubic centimetres instead of cubic metres. Keeping unit conversions clear at each step helps avoid these errors.

Final Answer:
The total volume of water that falls on the field is 750 cubic metres.