IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

mahendra_abd

problem- iron ball with redius 10 cm and coated with ice and melting rate of ice 50cm3/min so when the thinkness of ice 5 cm then the rate of decreses is how much
find the rate of melting when thinkness is 5 cm

iitkgp_bipin

Suppose at any instant the coating of ice has outer radius r.

Volume of ice, V = (4

/3)(r³ - 10³)

Differentiating this equation wrt time.
dV/dt = d[(4

/3)(r³ - 10³)]/dt = 4

r².(dr/dt)

Now you can find rate of change at different outer radii.

shakeel

volume V=4/3*pi*(r^3-10^3)

diff wrt time,

dV/dt = 4/3*pi*3r^2.dr/dt

hence dr/dt = {(4*pi*r^2)^(-1)} *dV/dt

when thickness=5 cm ,r=15 cm

dr/dt = {(4*3.14*15*15)^(-1)}*50

dr/dt = 0.1769

shakeel

sorry- 4got the unit

dr/dt = 0.1769 cm/min

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