Ex.11.3 Q14 Perimeter and Area - NCERT Maths Class 7

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Question

A circular flower garden has an area of \(314\rm\, m^2\). A sprinkler at the centre of the garden can cover an area that has a radius of \(12\rm\, m.\) Will the sprinkler can water the entire garden? (Take \(π = 3.14\)).

Text Solution

What is known?

A circular flower garden with an area of \(314\rm\, m^2\) and a sprinkler at the centre of the garden can cover an area that has a radius of \(12\rm\, m\)

What is the unknown?

Will the sprinkler water the entire garden?

Reasoning:

A circular garden has area of \(314\rm\, m^2\) and there is a sprinkler at the center of the garden which can water the area of radius \(12\rm\,m.\) So, first we have to find the area covered by the sprinkler. Compare the area covered by the sprinkler and the area of the garden. If the area covered by sprinkler is more that means it will sprinkle the entire garden.

Steps:

Area covered by the sprinkler

\[\begin{align} &= 2\pi r \\&= 3.14 \times 12 \times 12\\&= 452.16{\rm{ }}\rm\,{m^2}\end{align}\]

Area of the circular flower garden \(= 314\rm\, m^2\)

Since Area of circular flower garden is smaller than area covered by the sprinkler, the sprinkler will water the entire garden.