Use spherical coordinates to find the volume of the solid enclosed by the sphere x2 + y² + z² = 4a² and the planes z = 0 and z = a. NOTE: Enter the exact answer. V

Q: Find the area of the surface. The part of the sphere x? + y2 + z? = 25 that lies above the plane z =…

A: We have given The part of the sphere x2 + y2 + z2 = 25 that lies above the plane z = 2.

Q: Compote the volume of a reoion inside the Sphere x" +Y? +z² =4 ond between two sheets of the…

A: We have to find V0, V0 = Volume of sphere - V1-V2And from Symmetry we know that V1 = V2⇒V0 = Volume…

Q: Find the volume of the solid cut from the cylinder x? + y? = 100 by the planes z = O and a + z = 7.

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Q: Use spherical coordinates to find the volume of the solid. The solid enclosed by the sphere- + y? +…

A: Solution :-

Q: (a) Use the disk method to find the volume of the sphere x? + y? + z? = r. (b) Find the volume of…

A: (a).

Q: Use polar coordinates to find the volume of the given solid. Inside the sphere x?+ y² + z² = 25 and…

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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: 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, using spherical coordinates, the volume of the solid enclosed by the sphere x2 + y? + z2 = 9…

A: Here is the solution of the given problem. Volume bounded by the sphere and the plane z=2

Q: Using spherical coordinates, determine the volume of the solid that is above the z=2 v3 plane and…

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Q: Find the volume of the pyramid with base in the plane z = -11 and sides formed by the three planes y…

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Q: Use spherical coordinates to find the volume of the solid enclosed by the sphere x2 + y² + z2 = z =…

A: Using spherical coordinates: x=r cosϕ sinθy=r sinϕ sinθz=r cosθwhere:dx dy dz=r2sinθ dr dϕ…

Q: Using spherical coordinates, the volume of the solid inside the sphere x+y+z? -9 and above the plane…

A: Consider the given information,

Q: Use spherical coordinates to find the volume of the solid enclosed by the sphere x? + y? + z² = 4a?…

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Q: Use spherical coordinates to find the volume of the solid. The solid enclosed by the sphere X + y +…

A: Here, to find the volume if the solid enclosed by: x2+y2+z2=4a2 The cartesian to spherical…

Q: Using the spherical coordinate evaluate a) , x? dv, where G is a solid region between the sphere x?…

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Q: Use spherical coordinater to find the volume of the solid enclosed by the sphere a? +y? + z? : 4a?…

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Q: By double integral, find the volume of the solid enclosed by a paraboloid x + 2y2 + z = 16, the…

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Q: Using spherical coordinates, find the exact volume of the solid that lies within the sphere x? + y?…

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Q: Use spherical coordinates to find the volume of the top half of the sphere x? + y? + z? = 4 that…

A: Given that a sphere x2+y2+z2=4 and a cone is z2=x2+y2 We have to find the volume of the top of the…

Q: Use cylindrical coordinates to find the volume of the solid enclosed by the paraboloid z = x + y²…

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Q: Use spherical coordinates to find the volume of the solid enclosed by the sphere x2 + y² + z² = = 0…

A: Given :  x²+y²+z²=4a². And the planes z=0 and z=a   We have to find the volume of the solid using…

Q: the volume of the solid B that lies above the cone z = √√x² + y² and below the sphere x² + y² + z² =…

A: We will use relation between cartesian and spherical co ordinate to set up triple integral for…

Q: Use cylindrical or spherical coordinates, whichever seems more appropriate. Find the volume V of the…

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Q: Using spherical coordinates, the volume of the solid inside the sphere x+y+z²=9 and above the plane…

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Q: What is the volume of the following region, described in spherical coordinates? 1<p<9, 0 s

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Q: Use polar coordinates to find the volume of the given solid. Inside the sphere x2 + y2 + z? = 25 and…

A:

Q: Find the volume of the solid that lies inside both the cylinder x + y = 1 and the sphere a? + y? +…

A: Volume between given two shapes can be calculated by the method of triple integration.

Q: Calculate the volume of the sphere x^2 + y^2 + z^2 = a^2, using both spherical and cylindrical…

A: Given the equation of the sphere is       x2+y2+z2 = a2 ,where a is the radius of the sphere.

Q: Use cylindrical coordinates to find the volume of the solid enclosed by the paraboloid z = x² + y°…

A: Given

Q: Find the volume of the sphere x? + y² + z² = a² (In Cartesian coordinate system).

A: To calculate the volume of the sphere, use the following formulae.…

Q: Use cylindrical coordinates to find the volume of the solid enclosed by the paraboloid z = x² + y?…

A:

Q: Use polar coordinates to find the volume of the solid under the paraboloid z x²+y? and above the…

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Q: The base of a solid is the disk bounded by the circle x² + y? = r². Find the volume of the solid…

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Q: Using spherical coordinates, the volume of the solid inside the sphere x2+ y²+z2 =9 and above the…

A:

Q: Find the volume of the solid that lies under the hyperbolic paraboloid z = 3y? – x² + 4 and above…

A:

Q: Use polar coordinates to find the volume of the given solid. Inside the sphere x2 + y2 + z? = 36 and…

A:

Q: Use polar coordinates to find the volume of the given solid. Above the cone z = x² + y² and below…

A: Let D be the boundary D of the region enclosed by the cone z=x2+y2 and below the sphere x2+y2+z2=49,…

Q: Use cylindrical or spherical coordinates, whichever seems more appropriate.Find the volume V of the…

A: Given

Q: Use spherical coordinates to find the volume of the solid. The solid between the spheres x² + y² +…

A:

Q: Find the surface area of the portion of the sphere x² + y? + z² = 8 that is cut out by the cone z =…

A: The objective is to find the surface area of the portion of the sphere x2+y2+z2=8 that is cut out by…

Q: Use spherical coordinates to find the volume of the solid enclosed by the sphere x2 + y? + z2 = 4a?…

A: The complete solutions are given below

Q: Using spherical coordinates, the volume of the solid inside the sphere x+y? +z2 =9 and above the…

A: In spherical coordinates,  x=ρsinϕcosθ, y=ρsinϕsinθ, z=ρcosϕ, dxdydz=ρ2sinϕdρdϕdθ, x2+y2+z2=ρ2…

Q: Find the area of the part of Sphere x? + y? + z? = 16 that is outside the paraboloid z=16 – x² – y?.…

A: The part of the object outside another object can be obtained by first calculating the intersection…

Q: Use spherical coordinates to find the volume of the solid. The solid enclosed by the sphere X y² +…

A: We have to find the volume of the solid.

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: Find the volume of the first-octant portion of the "wedge" of the sphere x? + y? + z? = 64 bounded…

A: