A constant volume of pizza dough is formed into a cylinder with a relatively small height and large radius. The dough is spun and tossed into the air in such a way that the height of the dough decreases as the radius increases, but it retains its cylindrical shape. At time t = k, the height of the dough is inch, the radius of the dough is 12 inches, and the radius of the dough is increasing at a rate of 2 inches per minute. (a) At time t = k, at what rate is the area of the circular surface of the dough increasing with respect to time? Show the computations that lead to your answer. Indicate units of measure. Please respond on separate paper, following directions from your teacher. (b) At time t = k, at what rate is the height of the dough decreasing with respect to time? Show the computations that lead to your answer. Indicate units of measure. (The volume V of a cylinder with radius r and height h is given by V = ar² h.) %3D U Please respond on separate paper, following directions from your teacher. c) Write an expression for the rate of change of the height of the dough with respect to the radius of he dough in terms of height h and radius r.
A constant volume of pizza dough is formed into a cylinder with a relatively small height and large radius. The dough is spun and tossed into the air in such a way that the height of the dough decreases as the radius increases, but it retains its cylindrical shape. At time t = k, the height of the dough is inch, the radius of the dough is 12 inches, and the radius of the dough is increasing at a rate of 2 inches per minute. (a) At time t = k, at what rate is the area of the circular surface of the dough increasing with respect to time? Show the computations that lead to your answer. Indicate units of measure. Please respond on separate paper, following directions from your teacher. (b) At time t = k, at what rate is the height of the dough decreasing with respect to time? Show the computations that lead to your answer. Indicate units of measure. (The volume V of a cylinder with radius r and height h is given by V = ar² h.) %3D U Please respond on separate paper, following directions from your teacher. c) Write an expression for the rate of change of the height of the dough with respect to the radius of he dough in terms of height h and radius r.
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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A question out of a review sheet
![A constant volume of pizza dough is formed into a cylinder with a relatively small height and large
radius. The dough is spun and tossed into the air in such a way that the height of the dough decreases as
the radius increases, but it retains its cylindrical shape. At time t = k, the height of the dough is inch,
the radius of the dough is 12 inches, and the radius of the dough is increasing at a rate of 2 inches per
minute.
(a) At time t = k, at what rate is the area of the circular surface of the dough increasing with respect to
time? Show the computations that lead to your answer. Indicate units of measure.
Please respond on separate paper, following directions from your teacher.
(b) At time t = k, at what rate is the height of the dough decreasing with respect to time? Show the
computations that lead to your answer. Indicate units of measure. (The volume V of a cylinder with
radius r and height h is given by V = ar² h.)
%3D
U Please respond on separate paper, following directions from your teacher.
c) Write an expression for the rate of change of the height of the dough with respect to the radius of
he dough in terms of height h and radius r.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce08c4ed-eb77-44e7-b778-51357cdb5486%2F9e4abf07-f20c-4dd5-ade4-b2651e1b94e6%2F82dpltc.jpeg&w=3840&q=75)
Transcribed Image Text:A constant volume of pizza dough is formed into a cylinder with a relatively small height and large
radius. The dough is spun and tossed into the air in such a way that the height of the dough decreases as
the radius increases, but it retains its cylindrical shape. At time t = k, the height of the dough is inch,
the radius of the dough is 12 inches, and the radius of the dough is increasing at a rate of 2 inches per
minute.
(a) At time t = k, at what rate is the area of the circular surface of the dough increasing with respect to
time? Show the computations that lead to your answer. Indicate units of measure.
Please respond on separate paper, following directions from your teacher.
(b) At time t = k, at what rate is the height of the dough decreasing with respect to time? Show the
computations that lead to your answer. Indicate units of measure. (The volume V of a cylinder with
radius r and height h is given by V = ar² h.)
%3D
U Please respond on separate paper, following directions from your teacher.
c) Write an expression for the rate of change of the height of the dough with respect to the radius of
he dough in terms of height h and radius r.
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