Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 12.2, Problem 40PS
To determine
To find: the volume of the solid.
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2. Consider two spheres of equations r² + y² + z² 2x-2y + 4z-2 and x² + y² + ² = 4x+2y+4.
(a) For which points P on the first sphere and Q on the second sphere is the distance d(P.Q)
maximum?
ent
(b) Find the volume of the solid that lies inside both of the above spheres. (Hint: First show
that in a sphere of radius R the volume of a spherical cap (or spherical dome) of hight h is
V = ™h² (3R – h).)
2. Consider two spheres of equations x² + y² + z² = 2x - 2y + 4z -2 and x² + y² + z² = 4x+2y+ 4.
(a) For which points P on the first sphere and Q on the second sphere is the distance d(P,Q)
maximum?
(b) Find the volume of the solid that lies inside both of the above spheres. (Hint: First show
that in a sphere of radius R the volume of a spherical cap (or spherical dome) of hight h is
V = πh² (3R – h).)
3
2. Suppose you revolved the triangular region bound by the axes and
the line 4x + 3y
12 completely around the x-axis to sweep out
a solid of revolution. Describe the solid and then find its surface
area. Leave your answer exact.
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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Prob. 15PSCh. 12.5 - Prob. 16PSCh. 12.5 - Prob. 17PSCh. 12.5 - Prob. 18PSCh. 12.5 - Prob. 19PSCh. 12.5 - Prob. 20PSCh. 12.5 - Prob. 21PSCh. 12.5 - Prob. 22PSCh. 12.5 - Prob. 23PSCh. 12.5 - Prob. 24PSCh. 12.5 - Prob. 25PSCh. 12.5 - Prob. 26PSCh. 12.5 - Prob. 27PSCh. 12.5 - Prob. 28PSCh. 12.5 - Prob. 29PSCh. 12.5 - Prob. 30PSCh. 12.5 - Prob. 31PSCh. 12.5 - Prob. 32PSCh. 12.5 - Prob. 33PSCh. 12.5 - Prob. 34PSCh. 12.5 - Prob. 35PSCh. 12.5 - Prob. 36PSCh. 12.5 - Prob. 37PSCh. 12.5 - Prob. 38PSCh. 12.5 - Prob. 39PSCh. 12.5 - Prob. 40PSCh. 12.5 - Prob. 41PSCh. 12.5 - Prob. 42PSCh. 12.5 - Prob. 43PSCh. 12.5 - Prob. 44PSCh. 12.5 - Prob. 45PSCh. 12.5 - Prob. 46PSCh. 12.5 - Prob. 47PSCh. 12.5 - Prob. 48PSCh. 12.5 - Prob. 49PSCh. 12.5 - Prob. 50PSCh. 12.5 - Prob. 51PSCh. 12.5 - Prob. 52PSCh. 12.5 - Prob. 53PSCh. 12.5 - Prob. 54PSCh. 12.5 - Prob. 55PSCh. 12.5 - Prob. 56PSCh. 12.5 - Prob. 57PSCh. 12.5 - Prob. 58PSCh. 12.5 - Prob. 59PSCh. 12.5 - Prob. 60PSCh. 12.6 - Prob. 1PSCh. 12.6 - Prob. 2PSCh. 12.6 - 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Prob. 19PECh. 12 - Prob. 20PECh. 12 - Prob. 21PECh. 12 - Prob. 22PECh. 12 - Prob. 23PECh. 12 - Prob. 24PECh. 12 - Prob. 25PECh. 12 - Prob. 26PECh. 12 - Prob. 27PECh. 12 - Prob. 28PECh. 12 - Prob. 29PECh. 12 - Prob. 30PECh. 12 - Prob. 1SPCh. 12 - Prob. 2SPCh. 12 - Prob. 3SPCh. 12 - Prob. 4SPCh. 12 - Prob. 5SPCh. 12 - Prob. 6SPCh. 12 - Prob. 7SPCh. 12 - Prob. 8SPCh. 12 - Prob. 9SPCh. 12 - Prob. 10SPCh. 12 - Prob. 11SPCh. 12 - Prob. 12SPCh. 12 - Prob. 13SPCh. 12 - Prob. 14SPCh. 12 - Prob. 15SPCh. 12 - Prob. 16SPCh. 12 - Prob. 17SPCh. 12 - Prob. 18SPCh. 12 - Prob. 19SPCh. 12 - Prob. 20SPCh. 12 - Prob. 21SPCh. 12 - Prob. 22SPCh. 12 - Prob. 23SPCh. 12 - Prob. 24SPCh. 12 - Prob. 25SPCh. 12 - Prob. 26SPCh. 12 - Prob. 27SPCh. 12 - Prob. 28SPCh. 12 - Prob. 29SPCh. 12 - Prob. 30SPCh. 12 - Prob. 31SPCh. 12 - Prob. 32SPCh. 12 - Prob. 33SPCh. 12 - Prob. 34SPCh. 12 - Prob. 35SPCh. 12 - Prob. 36SPCh. 12 - Prob. 37SPCh. 12 - Prob. 38SPCh. 12 - Prob. 39SPCh. 12 - Prob. 40SPCh. 12 - Prob. 41SPCh. 12 - Prob. 42SPCh. 12 - 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- 2. Consider two spheres of equations x² + y² +22=2x-2y+4z-2 and x² + y² + z² = 4x +2y + 4. (a) For which points P on the first sphere and Q on the second sphere is the distance d(P, Q) maximum? (b) Find the volume of the solid that lies inside both of the above spheres. (Hint: First show that in a sphere of radius R the volume of a spherical cap (or spherical dome) of hight h is V = Th² (3R - h).)arrow_forward5. Find the volume of the solid generated by revolving about the x-axis the smaller area bounded by the equation x2+y²=2 and the semi-cubical parabola y3=x2. 6. Show that when a hole of radius a is bored through the center of the sphere of radius b, the volume of the sphere that is left is V= (4T/3)(b² - a²)(3/2)arrow_forward6. Find the volume of the solid under the surface (of the paraboloid) z = xy and above the triangle whose vertices are (0, 1), (1, 1) and (1,2).arrow_forward
- 6. Find the volume of the solid that lies within both the cylinder x² + y² = 1 and the sphere x² + y² + z² = 4. You must show all the work that leads to your final answer. Give the exact answer in simplest form.arrow_forward2. The closed region between the curves y² = 72 and y2 = 10 x in the first quadrant is rotated about the z-axis. 4 (a) The x-coordinate of the point where the curves intersect in the first quadrant is (b) The volume of the resultant solid of revolution is 5arrow_forward4. Find the volume of the solid enclosed by the surfaces z = 4 − x² − y², z = x² + 2y² − 2, x = −1, x = 1, y = -1 and y = 1.arrow_forward
- 4. A 3D solid has base that sits in the x-y coordinate plane. That base is a triangle with vertices (4, 0), (-4, 0), (0, 8). Cross sections perpendicular to the y-axis are semi-circles with diameter in the plane. The volume of the solid is given by A. * 7(8 – 2x)² dx B.,(2x + 8)? + f, (8 – 2x)²dx C. (8 – y)? dy D. (8 - y)? dy E. (8 – y)? dy 0 8 -8 T 0 4 -8 T 0 2arrow_forwardProblems: 1. Find the centroid for the area surrounded by the curve y=x', y-axis and the line y=8 ? 2. Find the centroid of the area enclosed between the line y=10-2x and the two Cartesian axis? 3. The area surrounded by the curve y=2x²-x+6, y-axis and the line y=9 represents a part of a solid area .Find its centroid? 4. Find the centroid of the shape shown in figure? 7 4 4 4arrow_forward
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