# In a rain-water harvesting system, the rainwater from a roof of \[22m\; \times 20m\] drains into a cylindrical tank having a diameter of base 2m and height 3.5 m. If the tank is full, find the rainfall in cm. Write your views on conversation.

Answer

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Hint- The quantity of rainfall in cm will be the height of the water body mentioned in cm formed over the same base area as from where it is catched (=collected).

Complete step-by-step solution -

Given in the question

Dimensions of rectangular roof

$l = 22m,b = 20m$

Where l is the length and b is the breadth

Dimensions of cylindrical tank

$r = 1m,h = 3.5m$

Where r is the radius and h is the height of the tank

The volume of the tank is given by

$

= \pi {r^2}h \\

= \dfrac{{22}}{7} \times 1 \times 1 \times 3.5 \\

= \dfrac{{22}}{7} \times \dfrac{{35}}{{10}} \\

= 11{m^3} \\

$

Now, area of the roof is given by

\[

= lb \\

= 22 \times 20 \\

= 440{m^2} \\

\]

The rainfall can be calculated as

$

{\text{Rainfall = }}\dfrac{{{\text{Volume of tank}}}}{{{\text{Area of roof }}}} \\

\therefore {\text{Rainfall = }}\dfrac{{11{m^3}}}{{440{m^2}}} = 0.025m \\

$

Hence, the rainfall in cm is 2.5 cm.

Note- To solve this type of question, remember all the formulas of area of rectangle, cylinder and circle and more. In this question we calculated the area of the roof and volume of the cylinder. Since, the volume occupied by rain in the cylinder must be equal to the volume occupied by rain on the roof. So, we calculated the volume of the cylinder and divided it by the area of the roof to get the height in cm of

Complete step-by-step solution -

Given in the question

Dimensions of rectangular roof

$l = 22m,b = 20m$

Where l is the length and b is the breadth

Dimensions of cylindrical tank

$r = 1m,h = 3.5m$

Where r is the radius and h is the height of the tank

The volume of the tank is given by

$

= \pi {r^2}h \\

= \dfrac{{22}}{7} \times 1 \times 1 \times 3.5 \\

= \dfrac{{22}}{7} \times \dfrac{{35}}{{10}} \\

= 11{m^3} \\

$

Now, area of the roof is given by

\[

= lb \\

= 22 \times 20 \\

= 440{m^2} \\

\]

The rainfall can be calculated as

$

{\text{Rainfall = }}\dfrac{{{\text{Volume of tank}}}}{{{\text{Area of roof }}}} \\

\therefore {\text{Rainfall = }}\dfrac{{11{m^3}}}{{440{m^2}}} = 0.025m \\

$

Hence, the rainfall in cm is 2.5 cm.

Note- To solve this type of question, remember all the formulas of area of rectangle, cylinder and circle and more. In this question we calculated the area of the roof and volume of the cylinder. Since, the volume occupied by rain in the cylinder must be equal to the volume occupied by rain on the roof. So, we calculated the volume of the cylinder and divided it by the area of the roof to get the height in cm of

Last updated date: 29th Sep 2023

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