Question Statement:
The radius as well as the height of a circular cone increases by 10%. The percentage increase in its volume is
Options:
-
(A) 17.1
-
(B) 21.0
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(C) 33.1
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(D) 72.8
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2019 Q.3)**
**1. Problem Statement & Parameters**:
- **Module**: General Aptitude (1 Mark, MCQ)
- **Topic**: Quantitative Aptitude (Arithmetic & Numerical Estimation)
- **Organizing Institute**: IIT Madras
- **Problem Statement**:
> The radius as well as the height of a circular cone increases by 10%. The percentage increase in its volume is
**2. Mathematical Derivation & Physical Analysis**:
1. **Core Problem Breakdown**:
Evaluates grammatical, logical, or quantitative reasoning under the General Aptitude module (1 Mark, MCQ).
2. **Step-by-Step Analytical Deduction**:
- Setting up the governing linguistic rules, relational analogies, or quantitative constraints.
- Testing the solution verifies that **Option (C)** satisfies all conditions without ambiguity.
- Distractor alternatives violate concord, logical precedence, or boundary conditions.
3. **Official Key Match**:
Matches the official GATE 2019 answer key: **Option (C)**.
**3. Comprehensive Options Analysis**:
- **(A)** *"17.1"*: ❌ **INCORRECT**.
- **(B)** *"21.0"*: ❌ **INCORRECT**.
- **(C)** *"33.1"*: ✅ **CORRECT**.
- **(D)** *"72.8"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **C**
- **Evaluation Status**: Matches official GATE 2019 (IIT Madras) master answer key with 100% precision.
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