Q6/ Find the volume of the parallclogram-sided determined by: u- -3i +7j +5k, v -3i + 7j-3k, and w- 7i-5j-3k.

Q: 4. Find the volume of the wedge cut from the first octant by the cylinder z = 12 – 3y², and the…

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Q: An open box is to be made out of a 10-inch by 20-inch piece of cardboard by cutting out squares of…

A: Draw the diagram for the given problem for the given conditions and then find the volume

Q: Find the volume of tetrahedron with vertices (0,0,0),(1,0,0),(0,1,0)and (0,0,2) by triple integral?…

A: We have to find the volume of the tetrahedrane with vertices 0,0,0, 1,0,0, 0,1,0 and 0,0,2 by triple…

Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

A: The given equation of plane is : x+2y+3z=6 x=6-2y-3z                   …(1) Volume of a rectangular…

Q: Find the volume of the tetrahedron in the first octant bounded by the coordinate planes and the…

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Q: Let's model R2-D2's body with a cylinder of height 3 feet and radius 0.75 feet and head with a…

A: Given, The radius of the cylinder = 0.75 feet The height of the cylinder = 3 feet The radius of the…

Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

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Q: Find the plane x/a + y/b + z/c = 1 that pass-es through the point (2, 1, 2) and cuts off the least…

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Q: Calculate the coordinates of the center of mass of the body delimited by the surfaces z = 9 - √x2 +…

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Q: Find  the Volumeof the largest rectangular box lying above the xy-plane, with y less that or equal…

A: considerlength of rectangular box =x width of rectangular box  =yheight of rectangular box =z

Q: what is the formula to find centroid of triangular prism

A: Centroid of triangular prism is determined as shown below.

Q: 3. What are the dimensions of the closed cylindrical can that has surface area 280 square…

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Q: find the centroid of volume if the volum is equal to 7/15 π

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Q: Determine the volume of the solid lying under the elliptic paraboloid z = 6y² – 2x² + 3 and above…

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Q: Find the area of the portion of the plane in the first octant passing through the points (0,0,6),…

A: This question can be solved using the area of triangle in three dimensional geometry.

Q: Calculate the volume of the solid above the xy plane delimited by = 9-x² - y²

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Q: Find the volume of the solid that is bounded by the cylinder z = 4x2, on the sides by the cylinder…

A: Let's find volume of solid.

Q: find the dimension of a cylinder that can be inscribed in a given sphere if it's convex surface area…

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Q: Estimate the volume of the solid that lies above the squareand below the elliptic paraboloid .…

A: The squares are shown below:

Q: Find the volume of the solid in the first octant bounded by 2x + 3y + 4z = 12 and the coordinate…

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Q: Use cylindrical coordinates to calculate the volume between the surfaces in the first octant if z =…

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Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

A: We first sketch the region using a graphing calculator. The shaded region will rotate about the…

Q: (1 point) Calculate the volume under the elliptic paraboloid z = 2x2 +3y2 and over the rectangle R =…

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Q: 6) Find the volume of the solid enclosed by the paraboloid z = 2--y and the plane z = 2.

A: According to question given that z=2-x2-y2z=-2

Q: Find the volume of the tetrahedron in the first octant that is bounded by the three coordinate…

A: The objective is to find the volume of the tetrahedron in the first octant that is bounded by the…

Q: The head of a steel meat tenderizer is cube with a side length of 5 centimeters. Once face of the…

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Q: Calculate the volume under the elliptic paraboloid z = 4x² + 6y2 and over the rectangle R = [-2, 2]…

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Q: Find the dimensions of the closed rectangular box with maximum volume that can be inscribed in the…

A: Let 2x, 2y, 2z be the dimensions of rectangular box. Then Let

Q: Find the volume of the solid in the first octant by bounded by the plane 3x +42 = 12, y = 2 and the…

A: Volume bounded by thefirst octent

Q: Calculate the volume of a water cylinder with total height of 10 meters, diameter of 400…

A: Radius of cylinder = Radius of Hemisphere = R = Diameter2 = 4002 = 200 cmTotal Height of container =…

Q: A closed rectangular box with faces parallel to the coordinate planes has one bottom corner at the…

A: Let x , y, z donate  the length, width and the height of the rectangular box.  Volume of the box is…

Q: Show that the rectangular box of maximum volume that can be inscribed in the sphere x^2 + y^2 + z^2…

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Q: Calculate the volume under the elliptic paraboloid z = 4x2 + 6y2 and over the rectangle R = [-2, 2]…

A: The solution for the above question is shown below.

Q: Find the volume of the solid that lies under the plane 4x+6y-2z+15=0 and above the rectangle…

A: Consider the given plane

Q: (Choose from: a. Disk Method, b.Washer Method, c. Shell Method, d. Disk and Washer, e. Disk and…

A: Given that, y = x2 ; x = 0; y = 15 3) Volume of the region bounded by the given curve rotated about…

Q: Find the volume of the solid bounded by the ellipic 4 + 5x² + 3y², the planes x paraboloid z = = 2…

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Q: Find the dimensions of the rectangular box of maximum volume that can be inscribed inside the sphere…

A: Given sphere is

Q: Find the volume of the solid bounded by surfaces z = /9-x2 - y2 , and z = /25 - x2 - y? and the…

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Q: Find the volume of the solid generated by revolving the pentagon with vertices (1, 0), (2, 2), (0,…

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Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

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Q: Find the volume of the wedge cut from the first octant by the cylinder x2 + y2 = 1 and the plane 2x…

A: To find the limits of x, y and z from the region of integration, substitute 0 for y.…

Q: Calculate the volume under the elliptic paraboloid z=3x2+7y2 and over the rectangle R=[−2,2]×[−4,4

A: Explanation: We know that,  Volume =∬zdydx By using the double integral concept, the volume of the…

Q: FiNd the volumes OF the solids gewerated by revolving +he regions bounded by the graphs oF the…

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Q: 6) Find the volume of the solid in the first octant bounded by the plane 3x +4z=12, y=2 and the 3…

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Q: Find the volume of the wedge cut from the first octant by the cylinder z=63-7y and the plane x+y=3

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Q: Find the volume of the region defined by the vectors. 7 -2

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Q: Find the volume of the solid bounded by the paraboloids z = – 5+ 2x2 + 2y² and z = 3 – 3x? – 3y? -

A: Here we use the cylindrical coordinate system to solve the problem.

Q: Consider the region in the first quadrant bounded by y=x^2, the y-axis, and y=4. -the y-axis using…

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Q: A right circular cylindrical container with volume 167 cm³ is to be made. Use the method of Lagrange…

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