Q81.If the volume of a spherical ball is increasing at the rate of 4π cc / sec then the rate of increase of its radius (in cm / sec), when the volume is 288π cc is (1) 1 (2) 1 9 6 (3) 1 (4) 1 24 36
What This Question Tests
This question tests the application of derivatives to find related rates of change, specifically how the radius of a sphere changes when its volume is increasing at a given rate.
Concepts Tested
Formulas Used
Volume of sphere V = (4/3)πr³
Chain rule for differentiation dV/dt = (dV/dr) * (dr/dt)
📚 NCERT Sections This Tests
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
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?
1.18 — A Point Charge Of 2.0 Mc Is At The Centre Of A Cubic Gaussian
Physics Class 11 · Chapter 1
1.18 A point charge of 2.0 mC is at the centre of a cubic Gaussian surface 9.0 cm on edge. What is the net electric flux through the surface?
📋 Question Details
- Chapter
- Applications of Derivatives
- Topic
- Rates of change
- Year
- 2014
- Shift
- 19 Apr Online
- Q Number
- Q81
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 6: Application of Derivatives
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