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Area, volume, and expantion

A.) let A be the area of a circle of radius r that is changing w/ respect to time. if dr/dt is a constant, is dA/dt a constant, explain.

b.) let V be the volume of a sphere of radius r that is changing w/ respect to time. If dr/dt is constant, is dV/dt constant, explain.

c.) All edges of a cube are expanding at a rate of 3 centimeters per second. How fast is the volume changing when each edge is a.) 1 centimeter b.) 10 centimeters?

Solution Preview

(a) A(t) = pi*r(t)^2
Now, dA(t)/dt = 2*pi*r(t)*dr/dt
Because dr/dt is constant, dA/dt is ...

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