Calculus

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Let V be the volume of a right circular cone having height h and radius r and assume that h and r vary with time.

a. Express the time rate of change of the cylinder in terms of h, r and their rates of change.
b. At a certain instant, the height is 10 in and decreasing at a rate of 1.5 in/sec, while the
radius is 3 in and increasing at a rate of 2 in/sec. How fast is the volume changing at
that instant and state whether the volume is decreasing or increasing.

  • Calculus -

    V is a function of r(t) and h(t)

    so use the product rule and chain rule:

    V(t)=(1/3)πr(t)²h(t)

    V'(t)=(1/3)π[2r*r'(t)]h(t)+(1/3)πr(t)²h'(t)

    Can you take it from here?

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