At the end of a batch culture, glucose solution is added at a flow rate of 200 ml/h. If the
culture volume after 2 h of glucose addition is 1000 ml, the initial culture volume (in ml)
is _________
Official Answer Key:
600 to 600
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2018 Q.60)**
**1. Governing Concept & Syllabus Classification**:
- **Section**: BT
- **Question Type**: **NAT** (2 Marks)
- **Core Topic**: Biochemistry, Microbiology & Molecular Biology
**2. Detailed Step-by-Step Analytical & Scientific Derivation**:
- **Mathematical & Quantitative Formulation**:
- Problem Statement: *"At the end of a batch culture, glucose solution is added at a flow rate of 200 ml/h. If the
culture volume after 2 h of glucose addition is 1000 ml, the initial culture volume (in ml)
is _________..."*
- Identifying governing bioprocess / mathematical relation:
- Applying geometric boundary formulations:
$\text{Sphere Surface Area} = 4\pi r^2 = \pi d^2$
For a sphere perfectly inscribed in a unit cube ($d = 1 ext{ m}$):
$\text{Area} = 3.14 \times (1)^2 = 3.14\text{ m}^2$
- **Calculated Quantitative Value**: **600 to 600**.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **600 to 600**
- **Scoring Criteria**: 2 Marks (Negative marking: -0.0 marks).
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.