Prove that the volume of the sphere x² + y² + z² = a² is V =÷na³

Q: Find the volume of the part of the ball p < 1 that lies between the cones o = 1/4 and ø = r/3. -1+ 2…

A: We have to find the volume of the part of the ball rho&lt;=1 that lies between the cones phi = π/4…

Q: Let B be the solid whose base is the circle (x^2) + (y^2) = (4^2)  and whose vertical cross sections…

A: This question is based on application of Integration.

Q: 2. Find the volume of the wedge cut from the cylinder r? + y? = 1 by the planes z = -y and z = 0.

A: Given the wedge cut from the cylinder x2+y2=1 by the planes z=-y and z=0.

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: Which of the following conditions do not have to be met to prove two solids have equal volumes using…

A: Given query is to find the condition which is not required to prove volume of solid are equal.

Q: Evaluate the volume between the surfac x²y, and the rectangle in the xy 2 = plane given by 2 < x <…

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Q: Find the volume of the paraboloid, z = 9 - x² - y², that lies inside the cylinder x² + y² = 4.

A: It is seen that the paraboloid and cylinder both are extended upto negetive infinity of along z…

Q: Find the volume of the solid bounded by the paraboloids z 9 + 3x2 + 3y and z = 7 - 3x? – 3y?

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Q: Use the Theorem of Pappus to find the exact volume of a general cone c with vertices (0, 0), (3, 0),…

A: Step:-1 Pappu's Theorem:- According to this theorem, the Volume V of a solid of revolution generated…

Q: (b) Find the volume under the paraboloid z-x+y above the triangle enclosed by the lines y=x,x-0 and…

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Q: 27. Find the volume of an ice cream cone bounded by the hemisphere z '8 – x² – y² and the cone z Va2…

A: Given hemisphere z=8-x2-y2 and cone z=x2+y2 The intersection of hemisphere and cone is given by…

Q: Find the volume of the solid in R' bounde y = x², x = y² , z = x + y + 33, and z V =

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Q: 25. Find the volume of the solid that is enclosed by the cone z = /x² + y² and the sphere x² + y² +…

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Q: ) show thet the pants ACいらり)。 B(2,2,2)) c(o,1,5) and D(1,0,5) are coplanear (in the Same plane). )If…

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Q: If the volume of the region bounded above by z = a2 − x2 − y2, below by the xy−plane, and lying…

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Q: Find the "volume" of the four-dimensional pyramid bounded by w +x+ y+z-1=0 and the coordinate planes…

A: The volume of the four dimensional pyramid is given by, V=∫v1 dv   =∫dzdydxdw. The boundaries are…

Q: Find the volume of the solid enclosed by the paraboloids z = 1 (x2 + y²) and z 32 – 1 (x2 + y²).

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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: verify that (u * v) . w = (v * w) . u =(w * u) . v and find the volume of the parallelepiped (box)…

A: Concept:…

Q: 3. Find the volume of the solid that lies between the paraboloid z = x² + y² and the sphere x2 + y²…

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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: b) Find the volume of the solid which is in the first octant and bounded between the spheres p = 1…

A: To find- Find the volume of the solid which is in the first octant and bounded between the spheres ρ…

Q: 9. Find the volume of the solid wedge cut from the first octant, bounded by the three coordinate…

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

A: Given: Equation of cone z=x2+y2 Equation of sphere x2+y2+z2=2

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 parallelepiped with adjacent edges t = 3j – 4j – 6k, u = 3i – 7j – 7k and v =…

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Q: Find the area of the portion, for which z > , of the sphere in R with radius v3 centered at the…

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Q: Prove that the volume of the sphere x2 + y² + z² = a² is V = na³ using triple integrals.

A: The formula to calculate the volume in spherical coordinate system is given below: V=∫ϕ∫θ∫ρρ2sinϕ dρ…

Q: 4 Calculate the directed curvilinear integral I where L is the perimeter of triangle ABC with…

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Q: Determine the volume of a four dimensional unit sphere: x, =r sin 8, sin 8, cos p, x, =r sin 0, sin…

A: The given problem is to find the volume of four dimensional unit sphere, we have to set up an…

Q: Find the volume of the solid bounded by the sphere x² + y² + =? = 6 and the paraboloid := x² +y² .…

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

Q: The volume of the parallelepiped is Volume = |a x b||c|| sin | = |(a × %3D b). c| True False

A: Using direct formula

Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u = 2i…

A: We have to find the volume of parallelepiped using scalar triple product for the given adjacent…

Q: need help with 9.2.5

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Q: Evaluate J CurIF. [cariF- nas F(x,v,z) = - yi + xj + zk, and S is part of the sphere z =9-x2 - y?…

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Q: (a) COMPUTE the dimensions of the rectangular box of maximum volume that can be x² + y? + z? = 4.…

A: Since you have posted multiple questions, we will solve only first question for you. To get…

Q: (b) Find the volume under the paraboloid z=x+y² above the triangle enclosed by the lines y=x, x=0…

A: To find the volume of the given solid.

Q: The volume of the parallelepiped is Volume = |a x b||c|| sin o| = |(a x b)- c| %3D %3D True False

A: We have to check either the volume of parallelepiped is volume=a×bcsinϕ=a×b·c or not.

Q: The net of a cone consists of three different two-dimensional areas. O True O False

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Q: Find the volume of the pyramid with the base in the plane z= -5 and the Sides formed by the three…

A: To find the volume of the pyramid

Q: Find the volume of the solid bounded by the sphere x2+y2+z2=6 and the paraboloid x2+y2=z.

A: Given Data The equation of the sphere is x²+y²+z²=6. The equation of parabola is x²+y²=z.   Let,

Q: Show that the volume of the segment cut from the paraboloid x2 /a2 + y2/ b2 = z/ c by the plane z =…

A: Show that the volume of the segment cut from the paraboloidX^2 /a^2 + y^2/ b^2 = z/ cby the plane z…

Q: Find the area of the part of the sphere x2 + y2 + z2 = a2 that lies inside the cylinder x2 + y2 =…

A: answer is A = a2(π -2) detailed solution with explanation is given below

Q: Show that the volume of the region bonded by the cone z=/x +y and the paraboloid z x+y is a/6.

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Q: Determine the volume of the largest rect an gu lar box in the first oct ant with three faces in the…

A: Given: The volume of the largest rectangular box is to be determined based on the first octant with…

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: he region bounded by the cylinder x2 + y2 = 9 and the planes z=0 and x +z =9 O 243 O 81T 27TT 729TT

A: Follow next step