Question

In a shower, 5cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
(a)75 cubic meter
(b)750 cubic meter
(c)7500 cubic meter
(d)75000 cubic meter

Answer 1

Hint: Convert the hectares and centimeters into meters. Then find the volume by the given area of the ground and the depth of the rainfall. We must get volume in \[{{m}^{3}}\], which is equal to cubic meters.

Complete step-by-step answer:
The hectare can be represented as ha. It is a non – SI metric unit of area equal to a square with 100 meter side of 1000\[{{m}^{2}}\] and is primarily used in the measurement of land.
Thus from the figure, you can understand that,
1 hectare = 100 m \[\times \] 100 m = 10000\[{{m}^{2}}\].
Similarly, 1.5 hectare = 1.5 \[\times \] 10000\[{{m}^{2}}\] = 15000\[{{m}^{2}}\]
Thus we got the area of land as 15000\[{{m}^{2}}\].
It is said that 5cm of rain falls. Thus the depth is 5cm. As the area is in meters, we need to convert the depth into meters.
\[\therefore \] 5cm \[=\dfrac{5}{100}\] meter = 0.05 meter.
We know that volume = length \[\times \] breadth \[\times \] depth.
Area = length \[\times \] breadth
\[\therefore \] Volume = Area \[\times \] depth.
We got an area as 15000\[{{m}^{2}}\] and depth as 0.05m.
\[\therefore \] Volume = 15000\[{{m}^{2}}\] \[\times \] 0.05m = 750 \[{{m}^{3}}\] = 750 cubic meter.
Thus the volume of water that falls on 1.5 hectare of ground is 750 cubic meter.
\[\therefore \] Option (b) is the correct answer.

Note: In this question we should know the basic metric system conversions between hectare, acre, meters and centimeters. Here the depth was in centimeters and area in hectare. Thus conversion of units is very important. If we find the volume without conversion of units, we will get the wrong answer.