Applications of Derivatives
Application of Derivatives
nta_pyq_2025_jan
Grade 12
Question:
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 cm /min and the thickness of the ice-cream layer 3 decreases at the rate of 1 4\pi cm/min . The surface area (in cm ) of the chocolate ball (without the ice-cream layer) 2 is :
196\pi
256\pi
225\pi
128\pi
Step-by-Step Solution
Key Concept: Apply the core result for monotonicity, tangents and extrema and simplify using the given constraints.
(2) 4 3 v = \pir 3 dv dr 2 = 4\pir dt dt 1 2 81 = 4\pir \times 4\pi 2 r = 81 r = 9 surface area of chocolate = 4\pi(r - 1) = 256\pi 2
Correct Answer: 2