The hyperbola x2 –y2=a2 revolves about its transverse axis. Find the volume of a segment of height a of the hyperboloid generated. Use the different method of Volume of Solid Revolution and dont forget to include figure

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 that lies under the hyperbolic paraboloid z = 3y2 - x2 + 4 and above…

A: The volume of the enclosed region under the, hyperbolic paraboloid z = f(x,y) and above the…

Q: A tank full of cooking oil has the shape of a paraboloid obtained by rotating a parabola about the…

A: We have given a paraboloid tank full of cooking oil. Height of tank = 4m. Radius at its top = 4m. We…

Q: Find the surface area of the part of the paraboloid z = 9 – 2.x - 2y that lies above the %3D

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Q: Find the area of the surface. The portion of the paraboloid  z = 49 − x2 − y2 in the first octant

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Q: The distance between the centers-of the following two spheres: x²-22x+y2-58y+z?=-961,…

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Q: Use the paramteric eauations of an ellipse, x=acos(theta), y=bsin(theta), 0<=theta<=2*pi, to find…

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Q: (b) Find the surface area of the portion of the paraboloid given by the equation z = 1- x? – y? that…

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Q: = Find the volume of the ellipsoid x² + y² + 6z² 64.

A: Given,                x2+y2+6z2=64.

Q: The axis of symmetry of the cylinder is parallel to the z-axis. х-ахis. O y-axis.

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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 that lies under the hyperbolic paraboloid z = 3y2 - x2 + 2 and above…

A: Given:z=3y2-x2+2 above the rectangle R=-1,1×1,5Formula:V=∬R z dx dy

Q: find the center of mass of a thin plate of constantdensity d covering the given region. The region…

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Q: Find the volume of the solid that lies under the hyperbolic paraboloid z = 3y² - x2 + 2 and above…

A: The volume of the solid that lies under hyperbolic paraboloid is:

Q: A cube with a cylinder cut from its center is cut along the plane shown. Which of the following is…

A: In this figure cube is just coated outside the cylinder

Q: Find the vollumes oF the solid that results when the r egion enclosed by the curves y= x, x = y is…

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Q: Find the center C and the radius a for the spheres x2 + y2 + z2 + 4x - 4z = 0

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Q: Q3: Find the volume of the solid enclosed by the parabola y = x? + 22 and the coney = 32 — x? — z2,

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Q: Find the area of the surface. The part of the hyperbolic paraboloid  z = y2 − x2  that lies between…

A: In the question we have to find the value of area enclosed by the function of given figures.

Q: Find the center and the radius of the sphere. 2 + y2 + z2 + 4x + 5z = 0

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Q: The volume of the tetrahedron enclosed by the coordinate planes and the plane 9x +y +Z = 18 is ?

A: We want to find the volume of the tetrahedron enclosed by the co-ordinate planes, i.e. x=0, y=0, z=0…

Q: A gasoline tank is an oblate spheroid generated by revolving the region bounded by the graph of…

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Q: Q3: Find the volume of the solid enclosed by the parabola y = x² +z? and the cone y = 32 – x² - z2.

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Q: A solid dome is to be constructed with the ellipse x^2+3y^2=6 as a base. Using infinitely many…

A: Graph the ellipse.

Q: Find the area of the plane region that lies below the line y = 2x and between the parabolas y= 2x^2…

A: Given Curves are:…

Q: Compute the volume of the ellipsoid obtained by rotating the ellipse 16 1 around the x-axis. O 40 O…

A: givenx216+y24=1this ellipse intersects x-axis at (4,0) and (-4,0)  becausex242+y222=1rewrite…

Q: 2 Find the volume of the ellipsoid 2y 7z 16

A: Volume of the ellipsoid for the equation,

Q: Determine the volume of the solid beneath the surface z = x^2 + y^2 that sits above the ellipse x2 +…

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Q: Find the volume of the ellipsoid x2a2+y2b2 +z2c2 =1.

A: Volume of the solid in region R is, V=∫∫∫RdV We know that spherical coordinate of ellipsoid is,…

Q: Find the surface area of the portion of the cone 22 = 4x² + 4y? nat is above the region in the first…

A: Given: The portion of the cone is Z2=4x2+4y2 which is bounded by the line y=x and the parabola y=x2

Q: Find the volume of the solid by subtracting two volumes, the solid enclosed by the parabolic…

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Q: Find the area of the ellipse cut from the plane z= 3x by the cylinder x + +y? =4

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Q: Find the area of the surface. The part of the paraboloid x = y² + z² that lies inside the cylinder…

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Q: Name the quadric surface: 2x-y²-z²=0 O Ellipsoid O Hyperboloid of one sheet фоалт 340095 t f quant

A: given quadratic equation 2x-y2-z2=0 claim- name the quadratic equation

Q: Find the surface area of the ellipse that lies on the plane z=11-3x+2y and inside the cylinder…

A: The plane z=11-3x+2y and cylinder is x2+y2=9. Obtain the partial derivatives of z=11-3x+2y:…

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: Find the volume of the solid that lies under the hyperbolic paraboloid z = 3y2 – x2 + 2 and above…

A: To find the volume of the solid that lies under the hyperbolic paraboloid  z=3y2-x2+2 and above the…

Q: (b) Find the volume and the surface area of the truncated cone made by the rotation of the solid…

A: Formula of cone: Volume of the cone, V=πr3h3 Surface area, A=πrs+πr2 where, r= radius of the base h=…

Q: Find the area of the ellipse cut from the plane z = 6x by the cylinder x + y = 9. .... Surface area…

A: Substitute the equation of plane in the cylinder equation

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 volume of the solid that lies under the hyperbolic paraboloid z=3y2−x2+2z=3y2−x2+2 and…

A: To find the volume of the solid the lies under the below hyperbolic paraboloid and above the…

Q: 5. Find the volume generated by the equation x2 +y² – 4x - 6y –- 12 = 0 if it is rotated about the…

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Q: Find the center and radius of the sphere. 2 4x + 4y + 4z + x + y+z= 25

A: Topic = Sphere

Q: • Find the area of the surface generated by revolving about the x-axis the upper half of the ellipse…

A: IN THIS QUESTION WE HAVE TO FIND AREA FROM REVOLUTION OF A ELLIPSE.

Q: 4. Find the area of ​​the surface of the revolution formed by rotating the part of the 4x^2 + y^2= 4…

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Q: Determine the volume of the solid lying under the elliptic paraboloid z = 6y? – 2x2 + 3 and above…

A: To evaluate the integral

Q: Identify the surface by completing the squares. x + 4y? – 2 – 6x + 8y + 4z = 0 O An elliptic…

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Q: 1 %3D 12 27

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Q: Identify the surface by completing the squares. x +16y² – z? – 14x + 32y + 8z = 0 O A hyperboloid of…

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.