Asked by Jay
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.
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.
Answers
Answered by
MathMate
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?
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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