How many plants will be there in a circular bed whose outer edge measure 30 cms, allowing 4 `cm^(2)` for each plant ?

Options

A. 18
B. 750
C. 24
D. 120

Answer

To solve the problem of how many plants can be planted in a circular bed with a circumference of 30 cm, allowing 4 cm² for each plant, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Circumference**:
The circumference of the circular bed is given as 30 cm.

2. **Use the Circumference Formula**:
The formula for the circumference (C) of a circle is:
\[ C = 2\pi r \]
where \( r \) is the radius.

3. **Set Up the Equation**:
We can set up the equation using the given circumference:
\[ 2\pi r = 30 \]

4. **Solve for the Radius**:
Rearranging the equation to find the radius \( r \):
\[ r = \frac{30}{2\pi} \]
Substituting \( \pi \) with \( \frac{22}{7} \):
\[ r = \frac{30}{2 \times \frac{22}{7}} = \frac{30 \times 7}{44} = \frac{210}{44} = \frac{105}{22} \approx 4.77 \text{ cm} \]

5. **Calculate the Area of the Circular Bed**:
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
Substituting the value of \( r \):
\[ A = \pi \left( \frac{105}{22} \right)^2 \]
Calculating \( \left( \frac{105}{22} \right)^2 \):
\[ A = \frac{22}{7} \times \frac{11025}{484} = \frac{22 \times 11025}{7 \times 484} = \frac{242550}{3388} \approx 71.59 \text{ cm}^2 \]

6. **Determine the Number of Plants**:
Each plant requires 4 cm². To find the number of plants \( N \):
\[ N = \frac{\text{Total Area}}{\text{Area per plant}} = \frac{71.59}{4} \approx 17.8975 \]
Rounding this to the nearest whole number, we get:
\[ N \approx 18 \text{ plants} \]

### Final Answer:
There will be approximately **18 plants** in the circular bed.