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A perfectly spherical snowball is melting over a cylindrical glass such that the radius of the snowball is reducing at a rate of ½ in/min. The glass has a radius of 3 in. How fast is the water level of the glass changing at the moment that the snowball's radius is 6 in?
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A step-by-step solution using Calculus notation is given.
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First, consider only the snowball, which is in the shape of a sphere.
Given: in/min when r = 6 in. Find:
Volume of a sphere is
Differentiate both sides of the equation with respect to t to get
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