H8upurpkaykochessy H8upurpkaykochessy

24-11-2016
Physics

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The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the diameter is 60 mm?

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Edufirst Edufirst

28-11-2016

V = [4/3]π r^3 => [dV / dr ] = 4π r^2

[dV/dt] = [dV/dr] * [dr/dt]

[dV/dt] = [4π r^2] * [ dr/ dt]

r = 60 mm, [dr / dt] = 4 mm/s

[dV / dt ] = [4π(60mm)^2] * 4mm/s = 180,955.7 mm/s

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