Approximations

Step 1: Formula Setup
Interval . Trapezoidal Rule: .
Step 2: Calculation
Distance . .
Final Answer: (b)

Step 1: Given Data
Error in diameter cm Error in radius cm. Radius cm.
Step 2: Formula for Percentage Error
Volume . .
Step 3: Calculation
Percentage Error .
Final Answer: (d)

Step 1: Concept
A general second-degree equation represents a circle if the coefficients of and are equal and the term is absent.
Step 2: Analysis
Cross-multiplying: .
Step 3: Evaluation
Integrating both sides: .
Step 4: Conclusion
For this to be a circle, the coefficient of must be 1 (same as ). So, .
Final Answer: (b)

Concept: Use linear approximation:

Step 1: Take .

Step 2: Compute .


Step 3: Find derivative.


Step 4: Apply approximation.
Conclusion:
Answer =