Q82.If the surface area of a sphere of radius r is increasing uniformly at the rate 8 cm2/s, then the rate of change of its volume is: (1) constant (2) proportional to √r (3) proportional to r2 (4) proportional to r dx is equal to:
What This Question Tests
The question requires setting up and solving a related rates problem using differentiation with respect to time for the surface area and volume of a sphere.
Concepts Tested
Formulas Used
S = 4πr²
V = (4/3)πr³
Chain rule for differentiation
📚 NCERT Sections This Tests
2.4 — A Spherical Conductor Of Radius 12 Cm Has A Charge Of 1.6 × 10–7C
Physics Class 11 · Chapter 2
2.4 A spherical conductor of radius 12 cm has a charge of 1.6 × 10–7C distributed uniformly on its surface. What is the electric field (a) inside the sphere (b) just outside the sphere (c) at a point 18 cm from the centre of the sphere?
3.9 — A Reaction Is First Order In A And Second Order In B.
Chemistry Class 11 · Chapter 3
3.9 A reaction is first order in A and second order in B. (i) Write the differential rate equation. (ii) How is the rate affected on increasing the concentration of B three times? (iii) How is the rate affected when the concentrations of both A and B are doubled? 85 Chemical Kinetics Reprint 2025-26
1.19 — A Point Charge Causes An Electric Flux Of –1.0 × 103 Nm2/C To Pass
Physics Class 11 · Chapter 1
1.19 A point charge causes an electric flux of –1.0 × 103 Nm2/C to pass through a spherical Gaussian surface of 10.0 cm radius centred on the charge. (a) If the radius of the Gaussian surface were doubled, how much flux would pass through the surface? (b) What is the value of the point charge?
📋 Question Details
- Chapter
- Applications of Derivatives
- Topic
- Rate of change of quantities
- Year
- 2013
- Shift
- 09 Apr Online
- Q Number
- Q82
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 6: Applications of Derivatives
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