Question

How many plants will be there in a circular bed whose outer edge measures \[30{\text{ cm}}\]allowing \[4{\text{ c}}{{\text{m}}^2}\]for each plant?
A) \[18\]
B) \[750\]
C) \[24\]
D) \[120\]

Answer 1

Hint:In the given question, we would first find the radius of the circular bed as the perimeter of the circular bed is given. Once, we calculate the radius, we would find the area of the circle. As we have the area of the plant already given in the question, we can calculate the total number of plants by dividing the area of the circular bed with the given area of each plant. If you get a floating value, you can match the answer to the closest value in the options.
Given, the outer edge of a circular bed is \[30{\text{ cm}}\].
Perimeter of a circle is the measurement of the outer edge of a circle.
Hence, the perimeter of the circular bed is \[30{\text{ cm}}\].
Perimeter can be calculated using the formula \[P = 2 \cdot \pi \cdot r\], where \[r\]is the radius of the circle.
We don’t know the radius of the circle, but can find the radius of the circle using the above formula and solve for \[r\].
So,
\[\begin{aligned}
  P = 2 \cdot \pi \cdot r \\
  30 = 2 \cdot \pi \cdot r \\
  \dfrac{{30}}{{2 \cdot \pi }} = r \\
  \dfrac{{15}}{\pi } = r \\
\end{aligned} \]
Area of the circular bed is equal to the area of the circle, that is, \[A = \pi {r^2}\].
\[\begin{aligned}
  A = \pi {\left( {\dfrac{{15}}{\pi }} \right)^2} \\
   = \dfrac{{225}}{\pi } \\
   \approx 77.59 \\
\end{aligned} \]
So, the area of the circular bed is \[77.59{\text{ c}}{{\text{m}}^2}\].
Given, each plant occupies \[4{\text{ c}}{{\text{m}}^2}\]. This means that the area occupied by each plant is \[4{\text{ c}}{{\text{m}}^2}\].
\[\begin{aligned}
  {\text{Total number of plants}} = \dfrac{{{\text{Area of the circular bed}}}}{{{\text{Area of each plant}}}} \\
   = \dfrac{{77.59}}{4} \\
   = 17.89 \approx 18 \\
\end{aligned} \]
So, 18 plants approximately will be there in the given circular bed.

Hence, option (A) is correct.

Note:
The total number of plants required to occupy the circular bed is always equal to the area of the circular bed divided by the area of each plant.