A spherical iron ball of radius 10 cm is coated with a layer of ice of uniform thickness that melts at a rate of ${\rm{50 c}}{{\rm{m}}^{\rm{3}}}/\min $. When the thickness of the ice is 5 cm, then the rate at which the thickness (in cm/min) of the ice decreases, is

JEE MATHEMATICS MCQ: RATE MEASURE

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A spherical iron ball of radius 10 cm is coated with a layer of ice of uniform thickness that melts at a rate of

\mathrm{50 c}{\mathrm{m}^\mathrm{3}}/\min

. When the thickness of the ice is 5 cm, then the rate at which the thickness (in cm/min) of the ice decreases, is

View answer and explanation

Correct option: B

\frac{1}{{18\pi }}

Option B (

\frac{1}{{18\pi }}

) is correct because it represents the rate at which the thickness of the ice decreases, calculated using related rates and the volume of a sphere.

Practice All Chapter MCQs →

v = 4\sqrt {1 + s}

v

s

m

{s^{ - 1}}

c{m^2}

4500 \pi

72 \pi

\frac{1}{2 \pi+16}

\mathrm{cm} / \mathrm{sec}

2 \mathrm{~cm}