The problem reads:

(b) If an error of 0.02 cm is made in measuring the side 10 cm of a square, then find the approximate percentage error in its area.

Solution:

1. Area of a square is given by $A = s^2$, where $s$ is the side of the square. For this square: $A = (10 \, \text{cm})^2 = 100 \, \text{cm}^2$

2. Percentage error in area can be approximated by using the formula for small errors: $\text{Percentage error in area} \approx 2 \times \frac{\text{Error in side}}{\text{Actual side}} \times 100\%$

   The error in the side is 0.02 cm, and the actual side is 10 cm. Plugging in the values: $\text{Percentage error} \approx 2 \times \frac{0.02}{10} \times 100\%$

3. Simplifying: $\text{Percentage error} = 2 \times 0.002 \times 100 = 0.4\%$

So, the approximate percentage error in the area is 0.4%.

Would you like more details or explanations on any part of the solution? Here are some related questions to expand on this:

1. How do we calculate the area of other shapes like rectangles or circles?
2. Why do we multiply the relative error by 2 for area calculations?
3. Can this error formula be applied to other geometrical shapes?
4. What would happen to the percentage error if the square’s side were measured incorrectly by 0.05 cm instead?
5. How does the error propagation change for higher powers or more complex functions?

Tip: The concept of error propagation is widely used in physics and engineering to estimate uncertainties in measurements and their effects on derived quantities.