A tube is being stretched while maintaining its cylindrical shape. The height is increasing at the rate of 2 millimeters per second. At the instant that the radius of the tube is 6 millimeters, the volume is increasing at the rate of 967 cubic millimeters per second. Which of the following statements about the surface area of the tube is true at this instant? (The volume V of a cylinder with radius r and height h is V = r2h. The surface area of a cylinder, not including the top and bottom of the cylinder, is S = 2πrh.) B The surface area is increasing by 287 square millimeters per second. The surface area is decreasing by 287 square millimeters per second. The surface area is increasing by 32π square millimeters per second.
A tube is being stretched while maintaining its cylindrical shape. The height is increasing at the rate of 2 millimeters per second. At the instant that the radius of the tube is 6 millimeters, the volume is increasing at the rate of 967 cubic millimeters per second. Which of the following statements about the surface area of the tube is true at this instant? (The volume V of a cylinder with radius r and height h is V = r2h. The surface area of a cylinder, not including the top and bottom of the cylinder, is S = 2πrh.) B The surface area is increasing by 287 square millimeters per second. The surface area is decreasing by 287 square millimeters per second. The surface area is increasing by 32π square millimeters per second.
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:A tube is being stretched while maintaining its cylindrical shape. The height is increasing at the rate of 2 millimeters per second. At the instant that the
radius of the tube is 6 millimeters, the volume is increasing at the rate of 967 cubic millimeters per second. Which of the following statements about
the surface area of the tube is true at this instant? (The volume V of a cylinder with radius r and height h is V = Tr2h. The surface area Sof a
cylinder, not including the top and bottom of the cylinder, is S = 2πrh.)
(A)
B
C
(D
The surface area is increasing by 28 square millimeters per second.
The surface area is decreasing by 287 square millimeters per second.
The surface area is increasing by 32π square millimeters per second.
The surface area is decreasing by 32π square millimeters per second.
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