Question

A spherical snowball with an outer layer of ice melts so that the volume of the snowball decreases at a rate of 2 cm^3/min . How fast is the radius changing when the radius of the snowball is 1 cm? The volume of a sphere of a radius r is (Explain in details your strategy to solve the problem and solve it.)

          A spherical snowball with an outer layer of ice melts so that the volume of the snowball decreases at a rate of 2 cm^3/min . How fast is the radius changing when the radius of the snowball is 1 cm?  The volume of a sphere of a radius r is  (Explain in details your strategy to solve the problem and solve it.)
        
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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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A spherical snowball with an outer layer of ice melts so that the volume of the snowball decreases at a rate of 2 cm^3/min . How fast is the radius changing when the radius of the snowball is 1 cm? The volume of a sphere of a radius r is (Explain in details your strategy to solve the problem and solve it.)
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Transcript

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00:01 Hi, today we are solving the question in which radius of snowball is 1 centimeter and rate at which it is decreasing.
00:10 So dr by dt is equals to minus 2 as it is decreasing.
00:15 So taking it as minus 2 cubic centimeters per minute.
00:19 Now we know that volume of the sphere is given by 4 by 3 pi r cube.
00:26 Now differentiating v with respect to t here.
00:30 So we get it as dv by d t is equals to 4 pi r square into d r by d t.
00:40 Now substituting the values...
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