Savita has a lamp placed at the centre of her square yard, each side measuring 20 m. The light of lamp covers a circle of radius 10 m on yard. What area of the yard is NOT lit by the lamp?

Options

A. `400 pi` sq. m
B. `100 pi` sq. m
C. `(40-10)pi` sq. m
D. `(400-100)pi` sq. m

Answer

To find the area of the yard that is not lit by the lamp, we can follow these steps:

### Step 1: Calculate the area of the square yard.
The area \( A \) of a square is given by the formula:
\[ A = \text{side}^2 \]
Given that each side of the square yard measures 20 m, we can calculate the area as follows:
\[ A = 20 \, \text{m} \times 20 \, \text{m} = 400 \, \text{m}^2 \]

### Step 2: Calculate the area covered by the lamp.
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
Here, the radius \( r \) of the circle covered by the lamp is 10 m. Thus, we can calculate the area as follows:
\[ A = \pi (10 \, \text{m})^2 = \pi \times 100 \, \text{m}^2 = 100\pi \, \text{m}^2 \]

### Step 3: Calculate the area of the yard that is not lit.
To find the area of the yard that is not lit by the lamp, we subtract the area covered by the lamp from the area of the square yard:
\[ \text{Area not lit} = \text{Area of square yard} - \text{Area covered by lamp} \]
Substituting the values we calculated:
\[ \text{Area not lit} = 400 \, \text{m}^2 - 100\pi \, \text{m}^2 \]

### Final Answer
Thus, the area of the yard that is not lit by the lamp is:
\[ \text{Area not lit} = 400 - 100\pi \, \text{m}^2 \]