# 3D Geometry Questions and Answers

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3D Geometry19 A local musician carries her portable speakers in a cylindrical container The dimensions of the container are shown in the drawing 15 in 3 in Which measurement is closest to the total surface area of the container in square inches A 424 12 in C 339 29 in B 791 68 in D 282 74 in

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3D GeometryIf the volume of a rectangular prism is V x 11x 36x 36 and one has a side length of x 6 what is the length of one of the other two sides O x 2 O x 3 x 6 O x 3

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3D GeometryTori is creating an informal argument for the formula for the volume of a square pyramid To start she considered a cube with side lengths of 10 units Then Tori sliced through the center of the cube along its diagonals creating identical square pyramids Tori s diagram is shown below 10 How many square pyramids did Tori slice the cube into What is the height of each square pyramid units Pick all the expressions that can be used to represent the volume of the square pyramid 10 10 10 10 10 5 10 10 10 10 10 5 10 10 10 10 10 6

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3D GeometryThe figure below shows a cone contained within a cylinder The tip of the cone touches the top of the cylinder 4 in Which of the following is closest to the volume of the space within the cylinder that is outside the cone A 6 in B 25 in 50 in C 151 in

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3D GeometryThis is an essay type question. Although Canvas provides space for you to type an answer, you do not need to type anything. This question will be graded completely based on the work that you submit at the end.
A. Find the equation of a sphere passing through the point (-1, 2, 4) with center (2, 5,1)?
B. Describe the intersection of this sphere with the xy-plane.

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3D GeometryTwo pyramids are similar with a ratio of surface areas of 25:64. Find the volume of the second pyramid given that the first has a volume of 250 m³.
A 61.0 m³
B 640 m³
C 1024 m³
D 97.7 m³
E 4194 m³

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3D GeometryFor the equation below, eliminate the xy-term and find the standard form of the conic in terms of x' and y'. Sketch the conic on the rotated axes. 41x²-24xy +34y²-25=0

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3D GeometryLet VC R5 be the subspace V
span {(1, 0, -3, 5, 0), (0, 2, 0, 0,3)} and let w = (-5, 0,5, -3, -4).
(a) Find the orthogonal projection of w onto V, using exact values in your answer.
(b) Find the component of w orthogonal to V using exact values.

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3D GeometryAssume that you want to approximate a function f(x, y, z)=x² + y² +2² by a line function ((x, y, z)= a₁x+ay+at+e such that f(x, y, z)=(x, y. 2) at four points (1,0,0), (1, 1.0), (0, 1, 1), a (1,0,1). Here, means that f(x, y, z) is almost equal to f(x, y, z). Your goal is to find the coefficients a₁.a. and c. Model this problem into an optimization problem of the form that minimizes the sum of squar errors between f and at these four points. Solve the resulting optimization problem.

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3D Geometry(b) What is the group of all symmetries of the tetrahedron, including those that
reverse orientation (and are therefore no longer rotations in 3-space)? (Hint: it's S₁. Why?)

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3D GeometryThe diagram represents a regular pentagonal pyramid. The measurements unit is feet. (Round your answers to two decimal places.)
(a) Find the area of the base.
ft²
(b) Find the lateral area of the pyramid.
ft²
(c) Find the surface area of the pyramid.
ft²
(d) Find the volume of the pyramid.
ft3

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3D GeometryFind an equation of the line where the planes Q and R intersect.
Q: -2x+3y-z = 1; R: x+y+z= -1
Choose the correct answer below.
A. An equation of the line is given by x = -5t, y = -1/5+4t,z=-4/5+t, where -∞<t<∞.
B. An equation of the line is given by x =-4/5+4t,y=-1/5+t,z=-5t,where -∞<t<∞.
C. An equation of the line is given by x =-5/4+4t,y=-5+3t,z=-2t,where -∞<t<∞o.
D. An equation of the line is given by x= -5+3t, y = -2t, z =-5/4-t,where - ∞<t<∞.

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3D GeometryWhich revolution will generate a cylinder? None of the other answers are correct Rotate a circle 360° about one of its diameters. Rotate a rectangle 360° about one of its diagonals. Rotate a circle 360° about one of its tangent lines. Rotate a rectangle 360° about one of its sides.

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3D GeometryIdentify the transformations. Sketch a graph of the following functions as a transformation of the graph of a toolkit function by first graphing the toolkit function, then the progression of transformations (in the correct order).
f(x) = -3(-x - 5)² + 4

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3D GeometryWhat is the exact volume of the solid stretching over the x-interval [0, 4] whose cross-sections are equilaterial triangles where the length of the side of a cross-section at x is given by the function
f(x)=√49-x²?
Note: Maintain fractions if applicable.