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AP Calculus AB/BC

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Sphere

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AP Calculus AB/BC

Definition

A sphere is a perfectly round three-dimensional object in which all points on its surface are equidistant from its center.

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Practice Questions (2)

The volume of a sphere is given by V = (4/3)πr^3. If the radius is increasing at a rate of 4 cm/s, what is the rate of change of the volume with respect to time when the radius is 3 cm?
The rate of change of the surface area of a sphere with respect to time is proportional to the square of the radius. At t = 0, the radius is 2 cm, and the rate of change of the surface area is 16 cm^2/s. If A(t) is the surface area of the sphere, what is the differential equation that represents this situation?

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