(c) Consider the parallelepiped with sides: u=(5,-2,1), v=(3,2, 4), and w=(-6,1,1). V (i) Find the volume of the parallelepiped.

Q: 3. Find the volume of the object cut from the cone z = Vx² + y² by the plane z = 1.

A: The volume of a solid can be obtained by considering a small volume element and integrating within…

Q: What is the volume of the solid enclosed by the planes z = 3 and x + y − z = −13, and the curves y…

A: Given,  The solid enclosed by the planes z = 3 and x + y − z = −13, and the curves y = x2 and x = y2

Q: Find the volume of the solid above the cone z2= 3(x2 + y2 ), z ≥ 0 and below the sphere x2+ y2+ z2 =…

A: We convert the units in spherical coordinate. The cone is given as,  The sphere is given as, The…

Q: 5a. Consider the right square pyramid with a horizontal plane intersecting the pyramid halfway up…

A: The horizontal plane will be parallel to the base of the pyramid.

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

A:

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 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: 2x2 dv, where T is the solid tetrahedron with verticies (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0,…

A:

Q: 7. If the net was folded into a box, which sides represent the lateral surfaces? a f C e d

A:

Q: Find the area of the surface. The part of the plane  z = 3 + 2x + 5y  that lies above the rectangle…

A:

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

A:

Q: Find the volume of the solid enclosed by the coordinate plane and the plane 2x + 3y + 6z = 6 using…

A:

Q: Find the volume of the ball x2+y2+z2≤R2.

A:

Q: Find the volume of the solid enclosed by the paraboloid z = 4 + x2 + (y – 2)2 and the planes z = 1,…

A:

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

A:

Q: Find the volume of the pyramid with base in the plane z=−5 and sides formed by the three planes y=0…

A:

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: The volume of the tetrahedron bounded by the coordinate planes and the plane x+y+z=4 is

A: Given

Q: Find the area of the surface. The part of the cylinder y2 + z2 = 9that lies above the rectangle…

A:

Q: Find the maximum volume of a box inscribed in the tetrahedron bounded by the coordinate planes and…

A:

Q: AP where R is the portion of the ball of radius 1 in 4-dimensions with all coordinates r, y, z, w 2…

A: I = ∫∫∫R∫ dvwhere R = portion of unit ball with x, y,z,w≥0I = ∫01∫01∫01∫01 dx dy dz dw= ∫01∫01yo1 dz…

Q: y = 8x2, x = 0, x = 4, and y = 0 Use the disk method to find the volume (in units3) when the region…

A:

Q: Find the volume of the solid enclosed by the paraboloid z = 5 + x2 + (y - 2)2 and the planes z = 1,…

A:

Q: 3. Find the volume of a solid enclosed by the parabolic cylinder y = x², the planes z = 0 and y +z =…

A:

Q: Find the area of the upper portion of the cylinder x2 + z2 = 1 that lies between the planes x = ±1/2…

A: Find the area of the upper portion of the cylinder x2 + z2 = 1 thatlies between the planes x = ±1/2…

Q: Find the area of the region formed by the lines: * - y, x = Jy, y = 0, y = 2 %3D O1.562 square units…

A: Explained below

Q: (b) Find the volume of the solid generated when R is rotated about the x-axis.

A:

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: Find the volume of the solid enclosed by the paraboloid z = 3 + x² + (y – 2)2 and the planes z = 1,…

A: Given z=3+x2+(y-2)2 and the planes z=1, x=-2,x=2,y=0 and y=2.

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

A:

Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

A:

Q: 3) Find the volume of the solid enclosed by the paraboloid z = r + y?- 4 and the plane 2 = 5.

A: We have to find out the volume of given paraboloid equation   z2=x2+y2-4    with plane   z=5

Q: Find the area of the surface. The part of the plane  z = 4 + 3x + 2y  that lies above the rectangle…

A: Consider the part of the plane that lies above the rectangle .

Q: 2 What Is the equatlon of the clrcle with a radius of 5 and center at (2, 3)? F (x + 2)2 + (y + 3)2…

A:

Q: e of the solid by subtracting two volumes, the solid enclosed by the parabolic cylinders y = 1 − x2,…

A: Here we have to find the volume of the solid  by subtracting two volumes, the solid enclosed by the…

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

A:

Q: Find the volume of the solid that lies under the hyperbolic paraboloid z = 20 + x² - y? and above…

A: We have given z = 20 + x2 − y2 and R = [−2, 2] × [0, 4]

Q: Find the area of the surface. The part of the plane z = 4 + 3x + 2y that lies above the rectangle…

A:

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: Find the volume of the solid enclosed by the paraboloid z = 5 + x + (y - 2)2 and the planes z = 1, x…

A:

Q: Find the area of the surface. The part of the plane z = 7+ 2x + 3y that lies above the rectangle [0,…

A: We have to find the area of the surface of the given problem.

Q: (A) Find the surface area of the portion of the half ball with radius a which cuts off by the…

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

Q: Calculate (x+ y)dA, where Ris a triangular region with vertices (0,0), (3,0) and (3,3).

A:

Q: Integrate G(x, y, z) = x + y + z over the surface of the cube cut from the first octant by the…

A: Definition used:

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: 1 %3D 12 27

A: