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A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.3cm/min. At what rate is the volume of the snowball decreasing when the diameter is 9 cm. (Note the answer is a positive number).

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ug80l4t9aa profile image

dD/dt = 0.3 cm/min

V = (4/3) pi r^3 = (4/3) pi (D/2)^3 = (4/3) pi D^3/8 = (pi/6) D^3

using the chain rule

dV/dt = (dV/dD)(dD/dt) = (pi/6) 3D^2 * dD/dt = (pi/2) (D^2) (dD/dt) = (pi/2) (9^2) (0.3) cm/min