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How many plants will be there in a circular bed whose outer edge measures $30cm$ allowing $4c{m^2}$ for each plant?
A). $18$
B). $750$
C). $21$
D). $120$

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Last updated date: 24th Jul 2024
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Answer
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Hint: A circle is a close two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. It is a round shaped figure. Every circle has radius and it is denoted by ‘r’. The line that intersects two points of the circle but doesn't pass through the center is known as “chord”.
As we know that area of circle
$ \Rightarrow A = \pi {R^2}$
Here,
A=Area of circle
R=radius of circle.

Complete step-by-step solution:
Given,
Circumference of circle, $P = 30cm$
As we know that
$\therefore P = 2\pi R$
Put the values
$ \Rightarrow 30 = 2 \times \pi \times R$
$ \Rightarrow R = \dfrac{{30}}{{\pi \times 2}}$
Simplify
$ \Rightarrow R = \dfrac{{15}}{\pi }cm$
Now area of circle,
As we know that
$ \Rightarrow A = \pi {R^2}$
Put the value
$ \Rightarrow A = \pi {(\dfrac{{15}}{\pi })^2}$
Simplify
$ \Rightarrow A = \dfrac{{225}}{\pi }c{m^2}$
One plant take $4c{m^2}$
Number of plants will be
$ \Rightarrow \text{number of plants} = \dfrac{{Total\,area}}{{area\,required\,for\,one\,plant}}$
Put the values
$ \Rightarrow \text{number of plants} = \dfrac{{\dfrac{{225}}{\pi }}}{4}$
Simplify
$ \Rightarrow \text{number of plants} = \dfrac{{225}}{{4 \times \pi }}$
$\therefore \pi = \dfrac{{22}}{7}$
$ \Rightarrow \text{number of plants} = \dfrac{{225 \times 7}}{{4 \times 22}}$
$ \Rightarrow \text{number of plants} = 17.89$
$ \Rightarrow \text{number of plants} = 17.89 \approx 18$
So the answer is (A) $18$.

Note: The coordinate axis divides the circle into the four parts known as quadrants. Labelled them as first, second, third and fourth. The perimeter of the circle is the length of the circle. When we make a circle from rectangular or square the area of the rectangle or square is equal to the perimeter of the square.