Find the volume of the tetrahedrons having the given vertices. TETRAHEDRON 1- (5, −3, 1), (5, −2, 4), (1, 1, 1), (0, 0, 1)   TETRAHEDRON 2- (1, 0, 0), (0, 1, 0), (0, 0, 2), (1, 1, 2)

Q: Find the volume of a solid obtained by rotating the region enclosed by the graphs x = 6 – 2y and x =…

A: Obtain the volume of the solid generated by rotating region bounded by x=6-2y and x=9-y2 about the y…

Q: The base of a certain solid is the triangle with vertices at (-6, 3), (3, 3), and the origin.…

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Q: An octahedron is a three-dimensional object that joins two square pyramids by their bases. Each…

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Q: A quadrilateral has vertices at (0,1,2), (3,0,1), (4,3,6), (2,3,2). Show that the volume of the…

A: A quadrilateral has vertices at (0,1,2), (3,0,1), (4,3,6), (2,3,2). Show that the volume of the…

Q: Time A solid is formed with a base that is a triangle with vertices at (0,0), (3, 0) and (0, 1).…

A: y-10-1=x-03-0  y-1=-x3y=1-x3

Q: 9. Find an expression in terms of x for the volume of this cuboid 3z - 1 2z - 3 5z +1 30z - 492 - 4z…

A: Concept: Volume of the cuboid is given by the formula: v=l×w×h

Q: Using the fact that the centroid of a triangle lies at the intersection of the triangle's medians,…

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Q: A pyramid 15 cm high is divided into three parts by two planes parallel to the base. These planes…

A: To determine the ratio of volumes, assuming the pyramid to be a square pyramid, consider vertical…

Q: The base of a region Is bounded between y = x + 1 and y = x² – 1, as shown in the figure. a) 1. Find…

A: Given that the base of a region is bounded between y=x+1 and y=x2-1 Since, the cross sections are…

Q: 56. Show that the six points (1, 0, 0), (−1, 0, 0), (0, 1, 0), (0, −1, 0), (0, 0, 1), and (0, 0, −1)…

A: Plotting given six points (1, 0, 0), (−1, 0, 0), (0, 1, 0), (0, −1, 0), (0, 0, 1), and (0, 0, −1).…

Q: The square region with vertices (14,0)​, (28,14)​, (14,28)​, and (0,14) is revolved about the​…

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Q: Find the volume of the region bounded above by the surface z = 9- y2 and below by the rectangle R:…

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Q: If two solids have the same height and all sections cut by planes parallel to their bases have equal…

A: 1). Decks of cards 2). Stacks of CDs 3). Coins one above other provide the same examples of equal…

Q: Quadrilateral UKEM has vertices U(-5,-1), K(-1,-1), E(-1,-6), and M(-5,-8). Determine the volume of…

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Q: Find the volume V of the solid obtained by rotating the region enclosed by the graphs of y = 18 –…

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Q: Derive the general formula for volume of x = x^3 , x-axis, x = 8 by circular disk method

A: Obtain the general formula for volume of y = x3, x-axis, x = 8 by circular disk method as follows.…

Q: A box with an open top has vertical sides, a square bottom, and a volume of 4 cubic meters. If the…

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Q: Find the volume of the solid obtained by rotating the region enclosed by the graphs about the line x…

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: Select all the choices that describe a right rectangular prism with a volume equal to 240 cubic…

A: the volume of the prism is given by area of base×height the given volume of the prism is 240 cubic…

Q: Determine the volume of the solid formed when a circle that passes through the points (l , 3), (3 ,…

A: As per the question we are given a circle passing through the three points : (1, 3) ; (3, 1) ; (1,…

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

A: Volume of tetrahedron

Q: find the volumes of the solids generated byrevolving the regions about the given axes. If you think…

A: Consider the following graph:

Q: An open box is made from a square piece material with sides 3 feet by 3 feet by cutting equal…

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Q: A pyramid 3 m high has a square base that is 3 m on a side. The cross-section of the pyra- mid…

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Q: Find the volume of the solid obtained by rotating the region enclosed by the graphs about the line x…

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Q: Let T be the polyhedron with vertices (1,0,0), (1,1,0), (1,1,1), (1,0,1) and (0,0,1). (img5) The…

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Q: Find the volume of the region bounded above by the elliptical paraboloid z=6-2²-2² and below by the…

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Q: 6. A new shed is going to be built. The volume of the shed must be 240 cubic feet. Determine…

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Q: An open cardboard box is to be made with a volume of 4m'. Find the dimension of the box that…

A: Volume has given, we use surface area of cardboard to solve following question

Q: Use integration to find the area of the triangular region having the given vertices. (0, 0), (2, 0),…

A: First of all, find the equations of a line with which the triangle is made. For that find the…

Q: The base of a three-dimensional figure is bound by the line x = -y - 2 on the interval [-5, -2].…

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Q: pyramid 3 m high has a square base that is 3 m on a side. The crosssection of the pyramid…

A: The pyramid is 3m high. Base of the pyramid is a square of side 3m. The cross section is also a…

Q: Find the volume of the region bounded above by the surface z=7-y and below by the rectangle R:…

A: The region given is z=7-y2. The volume will be calculated using the below integral. V=∬fx,ydA Where…

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

A: Given that  Plane x+7y+10z=70  To find the largest volume

Q: Solid Number of Faces Number of Edges Number of Vertices 1. Tetrahedron 2. hexahedron 12 12 5. 12…

A: Given, Solid Number of faces Number of edges Number of vertices 1.Tetrahedron…

Q: Find the area of the region bounded by the graphs of the given equations. y = 6x-x², y = - 2x The…

A: The given curves are: y=6x-x2, y=-2x   Now find the point of intersection between the given curves.…

Q: Find the volume of a solid obtained by rotating the region enclosed by the graphs x = 2 - y and x =…

A: The given curves are; x=2-y and x=4-y2 Now find the point of intersection between the given curves.…

Q: A rectangular box with an open top and one partition is to be constructed from 288 square inches of…

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Q: A vessel in the shape of a cone has a height of 48 cm and a base diameter 2 points of 16 cm. It…

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Q: An open box is to be made out of a 6-inch by 20-inch piece of cardboard by cutting out squares of…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: An open box is to be made out of a 12-inch by 14-inch piece of cardboard by cutting out squares of…

A: Given: The size of cardboard is 12-inch by 14-inch  To find the dimension of the resulting box that…

Q: Find the volume of thasparallelepiped with one vertex at the origin and adjacent vertices at (1,0, -…

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Q: The base of a three-dimensional figure is bound by the line x = y+2 on the interval [1, 9]. Vertical…

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Q: Use the Theorem of Pappus to find the volume of the given solid. The solid obtained by rotating the…

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Q: An open box is to be made out of a 12-inch by 14-inch piece of cardboard by cutting out squares of…

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Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, PS. P(2, 0, −1),    Q(3, 1, 2),…

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

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Q: An open cardboard box is to be made with a volume of 4m. Find the dimension of the box that requires…

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

A: The following figure represent the box,

Q: A box with an open top has vertical sides, a square bottom, and a volume of 4 cubic meters. If the…

A: Given: Volume = 4 m3