Use spherical coordinates to find the volume of the solid that is enclosed by the surface x+ y + z° = 2 and the planes z= 0 and z =1.

Q: Use spherical coordinates to find the volume of the solid bounded above by the sphere p = 4 and…

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Q: Use polar coordinates to find the volume of the region inside both the cylinder x² + y² = 4 and the…

A: The given curves are x2+y2=4                  (1)2x2+2y2+z2=9      (2)

Q: Compute the volume of the solid bounded by the hemisphere z = √√4c² - r² - y² and the horizontal…

A: Let's find volume of solid.

Q: What is the center of gravity of the solid formed when the plane region bounded by y = x^2 and y=x+2…

A: We sketch the given region using a graphing calculator as shown below:   The shaded region is…

Q: Use polar coordinates to find the volume of the solid enclosed by the surfaces z= 32• y² and z 6-3x2…

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Q: Compute the volume of the solid bounded by the hemisphere z = the horizontal plane z = c by using…

A: To compute the volume of the spherical cap, use the following formulae and convert the Cartesian…

Q: V4 – x2 – y² and the plane z = 0. Determine the volume of the solid enclosed by = Z

A: According to the problem, we have

Q: Sketch the region defined by the following two conditions (in spherical coordinates): 0<p<2, 0<¢s…

A: The region is: Given that 0≤ρ≤2, 0≤φ≤π4 The given region is a part of a sphere of radius 2.

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 that lies between the paraboloid z = x²…

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Q: Use spherical coordinates to find the volume of the solid enclosed by the sphere x2 + y² + z? = 4a?…

A: This question is about finding volume of solid enclosed by sphere. We can find it using triple…

Q: Use spherical coordinates to find the volume of the solid G bounded above by the sphere x² + y² + z²…

A: Given that the solid inside the sphere is x2+y2+z2=16 and  the cone is z=∠x2+y2we need to find the…

Q: Use cylindrical coordinates to find the volume of the solid that lies within the sphere…

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Q: Use polar coordinates to find the volume of the given solid. Enclosed by the hyperboloid -x² - y² +…

A: Here I am using polar coordinate and substution to solve this question. In this question we have to…

Q: Use spherical coordinates to find the volume of the solid bounded above by the sphere p = 2 /2 and…

A: First we have to set up a triple integral for the volume of the solid region bounded above by the…

Q: Use polar coordinates to find the volume of the given solid. Below the plane 5x + y + z = 8 and…

A: Given 5x + y + z = 8 and x2 + y2 ≤ 1

Q: Use polar coordinates to find the volume of the given solid. Enclosed by the hyperboloid -x² - y2 +…

A: Solution:-

Q: A closed surface is defined in spherical coordinates by 2 <r<4, <0 << < Find the volume enclosed. 18…

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Q: Express the volume of the solid lying inside the sphere r2 + y? + 22 8 and outside the cylinder ? +…

A: Given:  Solid lying in a sphere x2+y2+z2=16 and outside the cylinder  x2+y2=2

Q: Use polar coordinates to find the volume of the given solid. Enclosed by the hyperboloid -x² - y2 +…

A: Given To use polar coordinates to find the volume of the given solid enclosed by the hyperboloid…

Q: Use cylindrical coordinates to find the volume of the solid. solid inside the sphere  x2 + y2 + z2…

A: Given: The solid inside the sphere is: x2+y2+z2=1   -1 And, above the upper nappe of the cone is:…

Q: Find the volume of the portion of the ball æ² + y² + z² < 1 lying above the plane z = 3/5. (I would…

A: Intersecting point :  x2+y2+z2≤1,   z=35x2+y2+925≤1x2+y2≤452

Q: Find the coordinates of the center of gravity of the homogeneous wire showen below. The portion on…

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Q: Express the volume of the solid lying inside the sphere a? + y2 + 22 = 36 and outside the cylinder…

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Q: Use polar coordinates to find the volume of the solid that lies below the paraboloid f(x,y) = 36-…

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Q: Use cylindrical coordinates to find the volume of the solid that is bounded above by z = 6 and below…

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Q: Use polar coordinates to find the volume of the given solid. 21. Below the plane 2x + y + z= 4 and…

A: Given, The region D lies Below the plane 2x + y + z= 4 and above the disk x2 +y2 ≤1

Q: Compute the volume of the solid bounded by the hemisphere z = √√4c² - x² - y² and the horizontal…

A: hemisphere z=4c2-x2-y2 and plane z=cTo Find: Compute the volume of the solid using spherical…

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 spherical coordinates to find the volume of a solid that lies above the zy- plane, outside the…

A: The given 2 spheres are: x2+y2+z2=4…1x2+y2+z2=2z…2 The plane of intersection of the 2 spheres: To…

Q: Compute the volume of the solid bounded by the hemisphere z = √4c²-r² - y² and the horizontal plane…

A: The given problem is to find the volume of the solid bounded by given hemisphere and plane by using…

Q: Use cylindrical coordinates. JSS x² + y2 dv, where E is the region that lies inside the cylinder x²…

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Q: Explain why dz r dr dθ is the volume of a small “box” in cylindrical coordinates.

A: (r,θ,z) are the cylindrical coordinates; here r, θ denotes the polar coordinates of the image of…

Q: Compute the volume of the solid bounded by the hemisphere z = = √4c² - x² - y² and the horizontal…

A: The given problem is to evaluate the volume of the solid bounded by given hemisphere z=√(4c2-x2-y2)…

Q: Use polar coordinates to find the volume of the given solid. Below the plane 2x+y+z=4 and above the…

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Q: Use polar coordinates to find the volume of the solid under the paraboloid z = x2 + y2 + 1 and above…

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Q: Use polar coordinates to find the volume of the given solid. The solid above the xy-plane that lies…

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Q: Use spherical coordinate to find the volume above the cone z² = x² + y and inside sphere x² + y? +…

A: The equation of cone is, z2=x2+y2 The equation of sphere is, x2+y2+z2=2az

Q: Calculate, by means of cylindrical or polar coordinates, the volume of the solid that is inferiorly…

A: we have to find out the volume of the solid which is bounded below by  z=2y and above by…

Q: Use spherical coordinates to find the volume of the solid. Solid inside x2 + y2 + z2 = 81, outside z…

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Q: Use cylindrical coordinates to find the volume of the solid. Solid inside both x2 + y2 + z2 = 36 and…

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Q: Use cylindrical coordinates to find the volume of the solid. Solid inside both x2 + y2 + z² = 64 and…

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Q: use spherical coordinates to find the moment of inertia about the z-axis of the solid of uniform…

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Q: Use spherical coordinates to evaluate II. y dædydz, where V is the region with y > 0, z > 0, and x²…

A: To evaluate the given integral using spherical coordinates. Given integral is: ∭VydxdydzV is the…

Q: Compute the volume of W using cylindrical coordinates.

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Q: Use cylindrical shells when the region enclosed by the curves is revolved about the x- axis. (a) y =…

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

Q: Use spherical coordinates to calculate the volume of the region outside the sphere p = 2 cos Ø and…

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Q: Use spherical coordinates to find the volume of the solids: inside the sphere x^2 + y^2 + z^2 =9 and…

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Q: Compute the volume of the solid bounded by the hemisphere z = √4c²-x² - y² and the horizontal plane…

A: Here we will use spherical co ordinate to find volume of solid bounded between sphere and plane .…

Q: Use polar coordinates to find the volume of the solid below the paraboloid z=75−3x2−3y2z=75−3x2−3y2…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.