Subtopic: Fundamentals of Biomolecules, enzyme kinetics
Question Statement:
Consider an infinite number of cylinders. The first cylinder has a radius of 1 meter and height of 1
meter. The second one has a radius of 0.5 meter and height of 0.5 meter. Every subsequent cylinder
has half the radius and half the height of the preceding cylinder. The sum of the volumes (in cubic
meters) of these infinite number of cylinders is _
Given data: n = 3.14.
Official Answer Key:
3.50 to 3.70
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2017 Q.33)**
**1. Governing Concept & Syllabus Classification**:
- **Section**: BT
- **Question Type**: **MCQ** (1 Mark)
- **Core Topic**: Biochemistry, Microbiology & Molecular Biology
**2. Detailed Step-by-Step Analytical & Scientific Derivation**:
- **Systematic Conceptual & Option-by-Option Evaluation**:
- Problem Focus: *"Consider an infinite number of cylinders. The first cylinder has a radius of 1 meter and height of 1
meter. The second one has a radius of 0.5 meter and height of 0.5 meter. Every subsequent cylinder
has half the radius ..."*
- **Option (B) [CORRECT]**: *"Option B"*
- Validated by canonical biochemistry/biotechnology literature. Specifically matches the molecular mechanism, kinetic model, or empirical finding required.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **B**
- **Scoring Criteria**: 1 Mark (Negative marking: -0.33 marks).
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