Finding the Volume of a Parallelepiped In Exercises 69-72, find the volume
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Elementary Linear Algebra (MindTap Course List)
- Finding the Volume of a Tetrahedron In Exercises 41-46, find the volume of the tetrahedron with the given vertices. (0,0,0),(0,2,0),(3,0,0),(1,1,4)arrow_forwardA closed rectangular box with faces parallel to the coordinate planes has one bottom corner at the origin and the opposite top corner in the first octant on the plane 6x + 2y +z = 1. What is the maximum volume of such a box? volume = Submit answerarrow_forwardEXERCISE 4 A tetrahedron T is defined by its corner points (-1, -2, 4), (5, -1,0), (2, -3, 6), (1, –1, 1). Find the volume of T.arrow_forward
- Show all work!!arrow_forwardPlease solve thisarrow_forwardSurface Area of Solids using Nets Identify the shape that each net represents, and find its surface area. (use n = 3.14) Round your answer to two decimal places. 1) 3) 9 in Shape: Surface Area = Pás 9 in Shape: Syd 8 yd 6 in Syd Surface Area = 46 3yd Byd 9 in 5 yd 8 yd 5 yd 2) 5 yd 10 ft 4) 8 ft 10 ft Shape: 10ft Printable Worksheets @www.mathworksheets4kids.com Surface Area = 10 ft 9 in 12 ft Shape: Sheet 1 10 ft 12ft 10 ft Surface Area = 7 in 10 ft 10 ftarrow_forward
- (1) Compute the volume of a tetrahedron. (a) Illustrate the tetrahedron that has vertices at (0,0,0), (2,0,0), (0,4, 0), (0,0,6), in Cartesian coordinates. This tetrahedron sits inside a box with side lengths 2, 4 and 6. The volume of this box is V = 2 x 4 × 6 = 48 cubic units. The volume of the tetrahedron must be some fraction of this.arrow_forwardCal 3 HW 11.4 Q8arrow_forwardonsider the tetrahedron (a 4-sided pyramid whose faces are all triangles) with vertices atA = (1, 0, 0), B = (0, 2, 0), C = (0, 1, 3), and D = (2, 2, 0). Calculate the surface area and the volumeof the tetrahedron.(Hint: You may use the fact that the volume a tetrahedron is exactly one-sixth ofthe volume of the parallelepiped generated by the same vectors.) Surface Area = Volume =arrow_forward
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