Class IX Biology - Chapter: Cell - Topic: Magnification and Size Numerical Problems

Problem 1: Calculating Actual Size

A diagram of a cell shows its image size as 50 mm. If the magnification of the diagram is 500X, what is the actual size of the cell in micrometers (µm)?

Solution:

Magnification = Image Size / Actual Size

Rearranging the formula to find Actual Size: Actual Size = Image Size / Magnification

Given:

• Image Size = 50 mm
• Magnification = 500X

Actual Size = 50 mm / 500 = 0.1 mm

To convert millimeters to micrometers (1 mm = 1000 µm): Actual Size = 0.1 mm * 1000 µm/mm = 100 µm

Therefore, the actual size of the cell is 100 micrometers.

Problem 2: Calculating Magnification

An actual bacterium is 2 µm long. If its image under a microscope appears to be 10 mm long, what is the magnification of the microscope?

Solution:

Magnification = Image Size / Actual Size

First, ensure both sizes are in the same units. Let's convert millimeters to micrometers.

• Image Size = 10 mm = 10 * 1000 µm = 10,000 µm
• Actual Size = 2 µm

Magnification = 10,000 µm / 2 µm = 5000X

Therefore, the magnification of the microscope is 5000X.