The base of a solid is the disk bounded by the circle x² + y? = r². Find the volume of the solid given that the cross sections perpendicular to the x-axis are: (a) squares; (b) equilateral triangles.

Q: Find the volume of the cap of a sphere of radius r and height h for h < r.

A: The equation of the sphere with radius r is x2+y2+z2=r2. Determine z2 from the equation of sphere.…

Q: Find the volume of the torus generated by revolving the region bounded by the graph of the circle…

A: given x-112+y2=1 claim- to find the volume of torus generated by revolving the region bounded by the…

Q: Find the volume of the solid bounded below by the circular cone z = 2,/x² + y and above by the…

A: According to the given information, it is required to find the volume of the solid bounded below by…

Q: Find the volume of the solid obtained by rotating the triangle with the vertices A(0,0), B(4,4) and…

A: Solution

Q: Find the volume of the solid S whose base is the disk bounded by the circle x^2 + y^2 = r^2 and the…

A: Solution is given below:

Q: The base of a solid is the region bounded by the ellipse 4x2 + 9y? = 36. Find the volume of the…

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Q: A sphere of radius r is cut by a plane h units above the equator, where h &lt; r. Find the volume of…

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Q: The diameter and height of a paraboloid are 1 m and 2 m respectively. Determine its dimensions when…

A: Given, Diameterd=1 mHeighth=2 m The formula for finding the volume of the paraboloid is, V=π2hr2

Q: Use the Theorem of Pappus to find the volume of the solid of revolution. the torus formed by…

A:

Q: Find the volume of the solid above the cone z2= 3(x2 + y2 ), z ≥ 0 and below the sphere x2+ y2+ z2 =…

A: We convert the units in spherical coordinate. The cone is given as,  The sphere is given as, The…

Q: Use the disk method to verify that the volume of a sphere is 4/3 πr3 , where r is the radius ?

A: So sphere is basically a circle that is rotated through the x-axis. We will suppose to cut a disk…

Q: Use the Theorem of Pappus to find the volume of the solid of revolution The torus formed by…

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Q: Find the volume of the wedge cut from the first octant by the cylinder x? + y² = 1 and the plane 2x…

A: We have to find the volume of the wedge cut from the first octant by the cylinder x2+y2=1 and the…

Q: Find the volume of the solid whose base is the semicircle y = √9 - x² where -3 ≤ x ≤ 3, and the…

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Q: Find the volume of a solid where the base of the solid is  a circle with radius 2, and the cross…

A: Let the circle be centered at origin and the radius is 2.

Q: Use the Theorem of Pappus to find the volume of thegiven solid.A cone with height h and base radius…

A:

Q: Find the volume of the torus generated by revolving the circle (x - 2)^2 + y^2 = 1 about the y-axis.

A: Given: (x-2)2+y2=1

Q: Find the volume of the region enclosed by the cylinder x2 + y? = 2, the plane z – x+ y= 0 and the…

A: We have,

Q: Find the volume of the solid that is enclosed by the cone  z = sqrt(x2 + y2) and the sphere  x2 +…

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Q: Find the volume of the pyramid with base in the plane z=−5 and sides formed by the three planes y=0…

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Q: Use the Theorem of Pappus to find the exact volume of a general cone created by rotating a triangle…

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Q: The circle x2 + y2 = a2 is rotated about the x-axis to generate a sphere. Find its volume.

A: we have been given that the circle x2 + y2 = a2 is rotated about the x-axis to generate a sphere. we…

Q: The volume of the tetrahedron bounded by the coordinate planes and the plane x+y+z=4 is

A: Given

Q: Find the volume of the largest closed rectangular box in the first octant having three faces in the…

A: To Find: Volume of the largest closed rectangular box in the first octant having three faces in the…

Q: Determine the volume generated by revolving the plane figures about y axis. 4m 3m 1m 2m 4m 2m

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Q: The volume of the solid region, in the first octant, that lies below below the surface, z = above…

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Q: Find the volume of the tetrahedron bounded by the four planes x=0,y=0,z=0, and 2x+2y+x=4?

A: The equation of the plane 2x+2y+z=4  can be rewritten in the form  z=4-2x-2y let z=0, 0=4-2x-2y…

Q: Find the volume of the region enclosed by the paraboloid (x-1)²+y? =z and the plane 2x+z=2.

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Q: Use the Theorem of Pappus to find the volume of the solid of revolution The torus formed by…

A:

Q: Use the Theorem of Pappus to find the volume of the solid of revolution. the torus formed by…

A: We have to use theorem of pappus to find the volume of solid of revolution The torus formed by…

Q: The volume of the tetrahedron bounded by the coordinate planes and the plane x+y+z=2 is a. 2 Ob. 32

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Q: Determine the volume of the region that lies under the sphere x² + y² + z² = 4, above the plane z…

A: Given: Now,

Q: Find the volume of the solid whose base is the triangle enclosed by y-axis, y = 3, and y above…

A: First draw the base of the solid and find the cross section area then integrate.

Q: Find the volume of the ellipsoidal solid given by 4x² +4y² +z? = 16

A:

Q: Find the volume of the solid bounded below by the circular cone z = 3.51/x² + y and above by the…

A: To calculate the volume of the solid bounded below by the cone z=3.5x2+y2 and above by the sphere…

Q: Exercise 3. A cylinder with open top, closed bottom, radius r and height h has an outer surface area…

A: Given : Surfcae area of the open top cylinder is 8 cm²

Q: The base of a solid is the triangular region bounded by the y-axis and the lines 3x + 2y = 6 and 3x…

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Q: Use the disk method to verify that the volume of a right circular cone is (1/3)π r2h, where r is the…

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Q: The base of a solid is the region in the first quadrant bounded by the coordinate axes, and the line…

A: Volume of the solid

Q: Find the volume of the solid that lies under the elliptical paraboloid z = 2x2 + y? +4 and above the…

A: Given, z=2x2+y2+4 To find Volume of Solid

Q: Find the volume of the cap of a sphere with radius R and height h using a triple integral. R.

A: Consider the following figure By Pythagorean theorem x2+y2=R2 ⇒x2=R2−y2

Q: Use the Pappus Theorem to find the volume of the solid of revolution. The solid torus formed by…

A: the circle: (x − 7)2 + y2 = 16 = 42 Compare it with standard equation of a circle: (x - a)2 + (y -…

Q: Compute the volume lying inside the sphere x? + y? + z? = 37 but outside of x² + y? = 21.

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Q: Calculate the volume of the region bounded by the sphere a2 + y? + z? = 5 from above and by the cone…

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Q: Let a sphere of radius r be cut by a plane, thereby forming a segment of height h. Show that the…

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Q: A cone of height H with a base of radius r is cut by a plane parallel to and h units above the base,…

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Q: Use the theorem of Pappus to find the volume of a torus (pictured here). Assume that a disk of…

A: We know by the theorem of Pappu that the volume of a solid is obtained by area times the distance…

Q: Use the disk method to verify that the volume of a sphere is (4/3)π r3 , where r is the radius.

A: Volume of sphere of radius r is (4/3) πr3

Q: The volume of the tetrahedron bounded by the plane * ++ = :1, {a, b, c > 0} and the coordinate a…

A: Volume of the figure will be given by integral - V = ∫∫∫dzdydxLet's find limits of z,y and x - Given…