Q13.A spherical chocolate ball has a layer of ice-cream of uniform thickness around it. When the thickness of the ice-cream layer is 1 cm , the ice-cream melts at the rate of 81 cm3/min and the thickness of the ice-cream layer decreases at the rate of 1 cm/min. The surface area (in cm2 ) of the chocolate ball (without the ice- 4π cream layer) is : (1) 196π (2) 256π (3) 225π (4) 128π
What This Question Tests
This question is a related rates problem, requiring the application of the chain rule to relate the rate of change of volume and thickness of the ice-cream layer to find the radius of the chocolate ball, and then its surface area.
Concepts Tested
Formulas Used
V = (4/3)πR^3
A = 4πr^2
dV/dt = dV/dR * dR/dt
📚 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?
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?
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 (related rates)
- Year
- 2025
- Shift
- 23 Jan Shift 2
- Q Number
- Q13
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 6: Applications of Derivatives
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