The volume V of a right circular cylinder is given by the formula V= Tr h, where r is the radius and h is the height. (a) Find a formula for the instantaneous rate of change of V with respect to r if r changes and h remains constant. (b) Find a formula for the instantaneous rate of change of V with respect to h if h changes and r remains constant. (c) Suppose that h has a constant value of 4 in, but r varies. Find the rate of change of V with respect to r at the point wherer= 6 in. (d) Suppose thatr has a constant value of 8 in, but h varies. Find the instantaneous rate of change of V with respect to h at the point where h = 10 in.
The volume V of a right circular cylinder is given by the formula V= Tr h, where r is the radius and h is the height. (a) Find a formula for the instantaneous rate of change of V with respect to r if r changes and h remains constant. (b) Find a formula for the instantaneous rate of change of V with respect to h if h changes and r remains constant. (c) Suppose that h has a constant value of 4 in, but r varies. Find the rate of change of V with respect to r at the point wherer= 6 in. (d) Suppose thatr has a constant value of 8 in, but h varies. Find the instantaneous rate of change of V with respect to h at the point where h = 10 in.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:The volume V of a right circular cylinder is
given by the formula V= Tr h, where r is the
radius and h is the height. (a) Find a formula for
the instantaneous rate of change of V with
respect to r if r changes and h remains
constant. (b) Find a formula for the
instantaneous rate of change of V with respect
to h if h changes and r remains constant. (c)
Suppose that h has a constant value of 4 in, but
r varies. Find the rate of change of V with
respect to r at the point where r= 6 in. (d)
Suppose thatr has a constant value of 8 in, but
h varies. Find the instantaneous rate of change
of V with respect to h at the point where
h = 10 in.
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