Bladerunner1122
A sphere is increasing in volume at the rate 3pi cm^3/s. At what rate is its radius changing when the radius is 1/2 cm?



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sauravshakya
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V=4/3 pi r^3
dV/dt=d(4/3pi r^3)/dt

sauravshakya
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Now, use chain rule to find dr/dt

sauravshakya
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can u?

Bladerunner1122
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dr/dt = 1/(4pi r^2) * (dV/dt)

Bladerunner1122
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Substitute 1/2 in for r?

sauravshakya
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yes

sauravshakya
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and dV/dt=3pi cm^3/s

Bladerunner1122
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dr/dt = 1/(4pi*((1/2)^2))*3pi cm^3/s = 3 cm^3/s Thank you!! :)

sauravshakya
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welcome