A slide projector gives magnification of 10. If it projects a slide of 3 cm `xx` 2 cm on a screen, the area of image on screen is :

Options

A. `6000cm^(2)`
B. `600cm^(2)`
C. `3600m^(2)`
D. `2000m^(2)`

Explanation

To solve the problem, we need to find the area of the image projected on the screen by the slide projector, given its magnification and the dimensions of the slide.

### Step-by-Step Solution:

1. **Identify the dimensions of the slide**:
The dimensions of the slide are given as 3 cm by 2 cm.

2. **Calculate the area of the slide (object area)**:
\[ \text{Area of the object} = \text{length} \times \text{width} = 3 \, \text{cm} \times 2 \, \text{cm} = 6 \, \text{cm}^2 \]

3. **Understand the magnification**:
The magnification (M) of the projector is given as 10. This means that the image size is 10 times larger than the object size.

4. **Use the magnification to find the area of the image**:
The relationship between the area of the image (A_image) and the area of the object (A_object) can be expressed using the formula:
\[ M^2 = \frac{A_{\text{image}}}{A_{\text{object}}} \]
Rearranging this gives:
\[ A_{\text{image}} = M^2 \times A_{\text{object}} \]

5. **Substituting the values**:
\[ A_{\text{image}} = 10^2 \times 6 \, \text{cm}^2 = 100 \times 6 \, \text{cm}^2 = 600 \, \text{cm}^2 \]

6. **Final answer**:
The area of the image on the screen is \( 600 \, \text{cm}^2 \).