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

Q: Find the volume of the solid above the cone z = Vx² + y? and below the paraboloid z = 20 – x² – y?

A: Given For the given region, the paraboloid z=20-x2-y2 is the upper surface, and the cone z=x2+y2 is…

Q: Find the volume generated by the equation x? + y² – 4x – 6y – 12 = 0 if it is rotated about the line…

A: The volume of the solid generated by resolution can be calculated by calculating the surface area of…

Q: Find the volume of material cut from the solid sphere r2 + z2 <=9 by the cylinder r = 3 sin u.

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Q: What is the volume of this equation using the shell method? 2(pi)y((6/y+y^3)-(3/2(sqrt3))dy from the…

A: The volume for the given interval over the interval [1, sqrt3] can be computed as follows.

Q: Find the volume of the solid that lies above the cone z = Vx² + y? and inside the sphere x² + y² +…

A: To find the volume of a solid abov the cone  and inside the sphere Firstly find the region in…

Q: B) Show that V=367 is the volume of a sphere of radius 3 by using spherical coordinates.

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Q: Find the surface area of the sphere with radius of 7 in. Leave your answer in terms of T. 287 in 2…

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Q: Find the surface area of the part of the plane 4+ 2x + 3y that lies inside the cylinder x² + y? 9.

A: The area is given by using double integral

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 that lies inside both the cylinder x² + y² = 16 and the sphere x² + y²…

A: Given cylinder and sphere x2+y2=16x2+y2+z2=36 clearly, Here we need to find volume inside both…

Q: Find the volume of the region bounded above by the sphere r = 2a cos0, and below by the cone = a…

A: Given :             r =2a cosθϕ=α0 < α <π2  To Find : Volume of the bounded region

Q: Prove that the volume of a segment of height h of a sphere of radius r is V = }nh°(3r – h)

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Q: By integrating all three surface elements of a cylinder, find the surface area of a cylindrical pie:…

A:

Q: Use the disk method to evaluate the volume of the solid formed by rotating the area between…

A: Given,      Interval [ 2, ∞)

Q: Find the real number b such that the volume of solid B (r, +

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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 solid that lies under the elliptical paraboloid z = 2x? + y + 4 and above the…

A: V=∫∫RzdA V=∫01∫012x2+y2+4dydx Integrate with respect to y, V=∫012x2y+y33+y01dx…

Q: Find the volume enclosed by the cy linder (x-1) ty²=1 and the sphere x² +y²7z²=L4.

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Q: Use the Theorem of Pappus and the fact that the volume ofa sphere of radius r  is 4/3πr3  to find…

A: We have, The volume of a sphere is V=43πr3                               ⋯⋯1. The semi-circular…

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

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Q: f(x) = and the x-axis on the interval [2, 0) 7e*

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Q: Show by integration that the volume of a sphere of radius r is V=4/3 πr³

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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: Find the volume of the solid enclosed between the cone z = hr? and the plane z = 2h.

A: The variables in cylindrical coordinate systems are r, z and θ. In this problem, we have to find the…

Q: Use the disk method to verify that the volume of a right circular cone is 1/3 πr2 h, where r is the…

A: Given that: verify that the volume of a right circular cone is 1/3 πr2 h, where r is the radius of…

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: 4. Find the volume of the solid that lies within both the cylinder a²+y² = 1 and the sphere a2+y² +…

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Q: 5. Find the volume under the paraboloid = -a? – y?, and above the cone z = - p² + y?.

A:

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

A: Given: Now,

Q: Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the…

A:

Q: Find the volume of the solid that lies within the sphere x2 + y2 + z² = 36, above the xy-plane, and…

A: The sphere is x2+y2+z2=36 and cone is z=x23+y23. Substitute x=ρsinϕcosθ,y=ρsinϕsinθ,z=ρcosϕ in…

Q: Find the volume of the region enclosed by the cone z = x² + y² and the sphere r2 + y? + z² = 4.

A: Solve for volume

Q: Find the area of the upper portion of the cylinder x² + z? = 1 that lies between the planes x = ±1/2…

A:

Q: If a plane region R located in the first quadrant is revolved about the x-axis, then the measure of…

A: False.

Q: Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the…

A: We have to find the volume by using triple integral

Q: Use the change of variables formula to prove that the volume of the ellipsoid given by ()* + (#)* +…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

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

A:

Q: Determine the volume if the area common with y? – 3x +7y = 8 and x² – 4x + 3 = y² is revolved about…

A: Answer is mentioned below

Q: Find the surface area of a sphere of radius r

A:

Q: For the conical surface 0 = 30°,0 <0< 21,0 <r< 2, the lateral surface area is what?

A: Sol

Q: Find the volume of the solid that lies within the sphere x2 + y² + z² = 64, above the xy-plane, and…

A: To find the volume if the solid within the given sphere above xy-plane and below the cone:…

Q: Find the volume of the solid that lies within the sphere x² + y² +2²=81, above the xy plane, and…

A:

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: Find the volume of the first octant of the sphere x^2 +y^2 +z^2 = a^2 using dz dr d(theta)

A: Consider the sphere x2+y2+z2=a2. Therefore the given equation can be written as:…

Q: Find the volume of the solid enclosed by the cone z = sqrt(x2 + y2) between the planes z = 1 and z =…

A:

Q: Use triple integral to find the volume of the solid enclosed by the cylinder x2 + y² = 4, the sphere…

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Q: Find the volume of the solid that is enclosed by the cone z = and the sphere x² + y2 + z2 = 72.

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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