Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Question
Chapter 12.3, Problem 51PS
To determine
To find: The volume of the given solid region.
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Check out a sample textbook solutionStudents have asked these similar questions
18. The graph of x2/3 + y²/3 = 1 is called an astroid and is given be-
low. Find the volume of the solid formed by revolving the region
enclosed by the astroid about the x-axis.
x2/3 + y 2/3 = 1
-1
5) y=-4, y=x´– 4, x= 2
Axis: y = 2
y
Find the volume of the region that revolves around
the given axis.
Cis
1) Write and evaluate the definite integral that represents the volume of the solid formed by revolving the region about the x-axis.
y = −x + 4
2) Write and evaluate the definite integral that represents the volume of the solid formed by revolving the region about the x-axis.
y = x4, y = x7
3) Write and evaluate the definite integral that represents the volume of the solid formed by revolving the region about the y-axis.
y = √(9 - x2)
4) Find the volumes of the solids generated by revolving the regions bounded by the graphs of the equations about the given lines.
y = √x
y = 0
x = 6
(a) the x-axis
(b) the y-axis
(c) the line x = 6
(d) the line x = 9
5) Find the volumes of the solids generated by revolving the regions bounded by the graphs of the equations about the given lines.
y = x2
y = 6x − x2
(a) the x-axis
(b) the line y = 10
Chapter 12 Solutions
Calculus
Ch. 12.1 - Prob. 1PSCh. 12.1 - Prob. 2PSCh. 12.1 - Prob. 3PSCh. 12.1 - Prob. 4PSCh. 12.1 - Prob. 5PSCh. 12.1 - Prob. 6PSCh. 12.1 - Prob. 7PSCh. 12.1 - Prob. 8PSCh. 12.1 - Prob. 9PSCh. 12.1 - Prob. 10PS
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- YOUR TURN Find the volume of the solid of revolution formed by rotating about the x-axis the region bounded by y=x2+1, y=0, x=1 and x=1.arrow_forwardA soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.arrow_forwardPlease help and show all the steps. Thank you. The volume of a right circular cone of radius x and height y is given by V=1/3πx^2y. Suppose that the volume of the cone is 64π cm^3. Find dy/dx when x=4 and y=12 dy/dx=arrow_forward
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