3D Geometry Questions and Answers

Calculate the perimeter of the rectangle shown below Enter the value for the perimeter in the first blank and enter the units in the second Enter units as ft or square ft or cubic ft Round your final answer to tenths if rounding is necessary Them 7 4 ft CahaA 5 8 ft

An ellipse is formed when a plane slices through a cone Which of the following describes the relationship between the plane and the cone The plane is parallel to the base of the cone The plane is perpendicular to the base of the cone The plane is parallel to the slant edge of the cone and intersects the base of the cone The plane is at a slight angle with respect to the base of the cone but does not intersect it

3 1 point A crystal paperweight in the form of a square pyramid is represented by the figure below 4 9cm 6 cm What is the volume of the paperweight in cubic inches The volume of the paper weight is type your answer cubic inches

Unit F Representing 3 D Objects Chapter 11 Assignment 2 7 A friend took a picture of a plant she found in the mountains To give an idea of scale she put her camera lens cover in the picture beside the plant The lens cover has a diameter of 1 5 cm in the picture and the plant has a height of 4 5 cm If the lens cover has a diameter of 65 mm in real life what is the height of the plant to the nearest millimetre

19 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

If 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

Tori 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

The 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

This 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.

Two 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

For 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

Let 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.

Assume 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.

(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?)

The 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

Rewrite the following rectangular equation in polar form. y=3x

Find 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<∞.

Which 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.

Identify 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

The density of water is 1 gram per cm^3. An object floats in water if its density is less than water's density, and it sinks if its density is greater than water's. Will a toy in the shape of a rectangular prism that is 1 centimeter by 2 centimeter by 2 centimeter with mass 3 grams sink or float? Explain your reasoning.

Draw the shape, Find (b) period, (c) amplitude, (d) width, (e) shift (f) (x₀), x₁, x₂, x₃, x₄, x₅, and (g) sketch a graph of the function through one full period, . f(x) = – 3 sec(2πx + π/6) + 1.

Which of the following statements is true? Enter a, b, c, d, or e. a. All trapezoids are parallelograms. b. All squares are rectangles. c. All rhombus's are squares. d. Trapezoids are not convex. e. None of the above.

Which of the following statements is false? Enter a, b, c, d, or e. a. All squares are rectangles. b. All rhombuses are squares. c. All trapezoids are polygons. d. All rectangles are quadrilaterals. e. None of the above.

The original photograph shown is 4 inches by 6 inches. a. What transformations can you use to produce the new photograph? b. You dilate the original photograph by a scale factor of What are the dimensions of the new photograph? c. You have a frame that holds photos that are 8.5 inches by 11 inches. Can you dilate the original photograph to fit the frame? Explain your reasoning.

Brian made a rectangular prism with a length of 6 in., a width of 4 in., and a height of 8 in. If he doubled the height and width, what will be the volume of the new rectangular prism? The volume of the new rectangular prism is 68 times the original volume. The volume of the new rectangular prism is 6 times the original volume. The volume of the new rectangular prism is 4 times the original volume. The volume of the new rectangular prism is 2 times the original volume.

What is the volume of a sphere with a radius of 24.2 ft, rounded to the nearest tenth of a cubic foot?

What is the volume of a hemisphere with a diameter of 7.1 ft, rounded to the nearest tenth of a cubic foot?

The top of a gumball machine is a 20 in. sphere. The machine holds a maximum of 3,500 gumballs, which leaves about 56% of the space in the machine empty. Estimate the diameter of each gumball to the nearest whole number. The diameter of one gumball is about in.

A cylindrical fish tank at the zoo has a capacity of 7252 cubic feet. What is the height of the tank if its radius is 16 feet? Use = 3.14 and round to the nearest foot. 8 ft 9 ft 89 ft 144 ft

A cylinder has a radius of 4 it and a height of 6 ft. A cone has the same radius as the cylinder. Find the height of the cone if the two have the same volume. Leave in terms of Use pi for . Volume of cylinder = h= HET

If each edge of a cube measures 4 ft, how many pints of paint would it take to paint the entire cube if one pint of paint covers 25 square feet?

Sketch the graph of the surface z = 2x².

Determine whether the planes are parallel, perpendicular, or neither. 3x + 12y - 9z = 1, -15x + 30y + 35z = 0 parallel perpendicular neither If neither, find the angle between them. (If the planes are parallel or perpendicular, enter PARALLEL or PERPENDICULAR, respectively.)

Which statement below describes two polygons which are similar? a) Corresponding angles and sides are congruent. b) Corresponding angles are congruent and corresponding sides are proportional. c) corresponding angles and sides are proportional. d) Neither corresponding angles nor corresponding sides are congruent.

A right circular cone is inscribed inside a larger right circular cone with a volume of 200 cm³. The axes of the cones coincide, and the vertex of the inner cone touc the center of the base of the outer cone. Find the ratio of the heights of the cones that maximizes the volume of the inner cone. The ratio of the height of the inner cone to the height of the outer cone is

Ice Cream: An ice-cream cone has a radius of 2.3 cm and a height of 6.7 cm. The cone is filled with ice-cream and one additional scoop in the shape of a sphere with the same radius as the cone is placed on top. What is the amount of ice cream in cubic cm? Round to the nearest hundredth.

An aquarium tank (like at a zoo) measures 5.1 meters by 7.1 meters by 8.1 meters tall. The tank is filled to 1 foot below the top of the tank. Things you will need to do this problem (do NOT google to find other facts - use these facts): 1 ft = 0.3048 m There are 7.48 gallons in a cubic foot. The formula for the volume of this shape is length" width" height Sketch a picture of the tank and label the dimensions. It is likely easiest to do this on paper, scan and insert here either with cut/paste or the insert image button above (mountain icon).

3. Use the diagram to answer the following questions. a) How many points appear in the figure? b) How many lines appear in the figure? c) How many planes appear in the figure? d) Name three collinear points. e) Name four coplanar points. f) Name the intersection of planes ABC and ABE. g) Name the intersection of planes BCH and DEF. h) Name the intersection of AD and DF. \\

A can of soup weights 12.5 ounces. You decide you want to find the density of the soup. The cylindrical can of soup is 5 inches high with a radius of 1.5 inches. What the density of the soup? Use pi = 3.14 and round to two decimal places. 2.86 ounces/in 0.35 ounces/in³ 0.35 ounces/in² 2.86 ounces/in"

litem Which of the following are parameterizations of the line that is the intersection of the planes given by the equations x - 2y + z = 2 an x - z = 0? (x, y, z) = (t + 1, −2t, t+1) (x, y, z) = (t + 1, -2t, t - 1) (x, y, z) = (t, t - 1,t) (x, y, z) = (t + 1, t, t+1) (x, y, z) = (t +2, t+1, t+ 2)

A plane passes through the point (1,0,- 2) and is perpendicular to the vector < 2,1,- 3>. (3 points) a. Find the equation of the plane. (1 point) b. Find the z-intercept of the plane. (2 points)

Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves and the specified axis. Make sure to draw the region in question. a.) x = -3y² + 12y-9, x = 0; about x-axis b.) x = 2y², x = y² + 1; about y = -2

X X If a company needs to create a box out of a piece of cardboard that has a length of 8 inches and a width of 6 inches. Select the function that represents V (x), the volume of the box. O V(z) = 2 (8-2x) (6-2) O V(z) = (8-2x) (6-2x) O V(x) = x + (8-2x) + (6-2x) O V(x) = x (8+2x) (6 + 2x)

The figure shows a sphere and a plane. When a plane intersects a sphere, which phrase best describes the possible intersections that result? a point or a circle a circle or an ellipse a rectangle or a point a parallelogram or a point

A right circular cone has a radius of 2x + 4 and a height `1` units less than its radius. Express the volume of the cone as a polynomial function. The volume of a cone is 'V = 1/3 pi r^2 h for radius r and height h. Enter π as pi.

The diameter of a cylindrical construction pipe is 4 ft. If the pipe is 22 ft long, what is its volume? Use the value 3.14 for π, and round your answer to the nearest whole number. Be sure to include the correct unit in your answer.

The diameter, D, of a sphere is 13.8 cm. Calculate the sphere's volume, V. Use the value 3.14 for it, and round your answer to the nearest tenth. (Do not round any intermediate computations.)

An ellipse is formed when a plane slices through a cone. Which of the following describes the relationship between the plane and the cone? The plane is parallel to the base of the cone. The plane is perpendicular to the base of the cone. The plane is parallel to the slant edge of the cone and intersects the base of the cone. The plane is at a slight angle with respect to the base of the cone, but does not intersect it.

Find the length of a side of a square whose diagonal is 10 in. long. Round your answer to the nearest hundredth. The length of a side of a square is

Alyssa is designing a cone to scoop water from a tank. She figured that the scoop should hold approximately 66 in³ of liquid. The diameter of her cone is 6.5 in. What should be the height of the cone? Round your answer to the nearest whole number. 6 inches 2 inches 1 inch 5 inches