A circular garden having a radius of 28 cm. If 80% of it is cultivated, what is the area of garden remaining uncultivated?

The correct option is 492.8 cm².

To find the area of the garden that remains uncultivated, we first determine the total area of the circular garden and then calculate the uncultivated percentage.

Step 1: Understand the given parameters
Radius of the circular garden, r = 28 cm
Percentage of area cultivated = 80%

Step 2: Calculate the uncultivated percentage
The total area of the garden corresponds to 100%.
Uncultivated percentage = 100% - 80% = 20%

Step 3: Calculate the total area of the circular garden
The formula for the area of a circle is:

$\text{Area}=\pi \times r^2$

Using π = $\frac{22}{7}$:

$\text{Total Area}=\frac{22}{7}\times 28\times 28$

$\text{Total Area}=22\times 4\times 28$

$\text{Total Area}=2464{\text{cm}}^2$

Step 4: Calculate the uncultivated area
Now, find 20% of the total area:

$\text{Uncultivated Area}=20\%\times 2464$

$\text{Uncultivated Area}=\frac{20}{100}\times 2464$

$\text{Uncultivated Area}=\frac{1}{5}\times 2464$

$\text{Uncultivated Area}=492.8{\text{cm}}^2$

Therefore, the area of the garden remaining uncultivated is 492.8 cm².