Question

On a particular day, the rainfall recorded in the terrace is 6m long and 5m board is \[15cm\]. The quantity of water collected in then terrace is
A) \[300{\text{ }}litres\]
B) \[450{\text{ }}litres\]
C) \[3000{\text{ }}litres\]
D) \[4500{\text{ }}litres\]s

Answer 1

Hint: In the given question, we are asked that on a particular day, the rainfall recorded in a terrace having some specific dimensions. Therefore we are to find out the quantity of water recorded in the terrace. Firstly we will check the dimensions and shape of the terrace and then use the formula to find out the quantity of water collected in the terrace.

Complete step-by-step answer:
In the given question, we are given that terrace is having dimensions than on a particular day, rainfall is recorded or collected on the terrace which is found to be\[\;6m\]long, \[5m\] broad and high which means the length of rainfall recorded in the terrace is \[\;6m\] long, breadth of rainfall recorded is \[5m\] broad and height of rainfall recorded is \[15cm\] high.
Now, we have to find out the quantity of water collected on the terrace. Since length, breadth and height are given. Therefore we have to find out the quantity or volume of the rainfall recorded.
Given \[length{\text{ }} = {\text{ }}6m,{\text{ }}breadth{\text{ }} = {\text{ }}5m{\text{ }}and{\text{ }}height{\text{ }} = {\text{ }}5cm\]. Firstly we have to convert height from \[cm\] to \[m\]
Also \[1m{\text{ }} = {\text{ }}100cm\]
Therefore \[1cm{\text{ }} = {\text{ }}\dfrac{1}{{100}}m\]
Now \[15cm\] in height
Therefore \[15cm = \dfrac{{15}}{{100}} = 0.15m\]
Now, Volume = \[length \times breadth \times height\]
\[ \Rightarrow \left( {6m \times 5m \times 0.15m} \right)\]
\[ \Rightarrow 4.5{m^3}\]
Since quantity to find out. Therefore \[{m^3}\] should be converted to litre. Also we know the relationship between \[{m^3}\] and litre.
So, \[1{m^3} = {\text{ }}1000{\text{ }}litre\]
\[ \Rightarrow Volume{\text{ }} = 4.5 \times 1000{\text{ }}litre\]
\[ \Rightarrow 4500{\text{ }}litres\]
Therefore, a quantity of water collected in the terrace is 4500 litre
So option (D) is correct.

Note: The rainfall water is collected in the terrace since the terrace is in the form of a cuboid. So rainwater collected on the terrace also took the shape of a cuboid. This can be explained as water collected in the cylinder took the shape of a cylinder. Also, the same water collected in the spherical bowl took the shape of a sphere.