3D Geometry Questions and Answers

A manufacturer makes decorative globes out of silver in the shape of a solid sphere. Suppose each sphere has a radius of 3 cm. If silver is priced at $7.00 per cm^, 3 how much will the silver cost to make one solid sphere?

Consider two planes P₁: 2x - 3y + z = -5 and P2 : x - 4y - 14z = 5. If a line L perpendicular to P₁ whose one point A(-7, y₁, z₁) lies on plane P₁ and point B(x2, Y2, Z2) and C(X3, y3, Z3) lies on plane P2 as well as on line L. Value of Z3-Z2/ Y3-Y2+ X3-X2/ Z3-Z2 is +

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?

23. A rectangular prism (box) has dimensions 8 cm by 10 cm by 15 cm. Part A. What is the total surface area of the box? (Hint: Combined area of all faces.) Part B. What is the volume of the box?

The radius of a sphere is increasing at a rate of 7.5 meters per minute. At a certain instant, the radius is 5 meters. What is the rate of change of the surface area of the sphere at that instant (in square meters per minute)?

Cardi O went to a party and drank alcohol. She estimated that her blood alcohol content (BAC) was 0.16. BAC decreases by 25% every hour. a. Is this situation describing a linear or exponential decrease? b. Write several sentences to convince me of your answer.Write a function describing this situation. c. Sketch the graph of the function and label the y-intercept (Hint: It might help to start by making a table.) d. Cardi O knows a safe driving level for someone of her weight is 0.04. How long does she need to hang out with her friends (without drinking any more alcohol) before it is safe for her to drive? Show or explain your method for finding this solution.

On a separate sheet of paper, draw a picture of an isosceles triangle and label it. Then draw a picture of a scalene triangle and label it. Submit the images of the triangles below.

A plane in the xyz-coordinate system is has the equation 3x - 6y + 2z = 6. a. Find the x-intercept, y-intercept, and z-intercept of the plane. b. Find the equation of the plane which is parallel to 3x -6y + 2z = 6 and contains the point (1,1,1).

If the volume of a cone is 294 in^3 and the height of the cone is 14 inches, what is the radius? Round to two decimal places and use pi = 3.14. 6.69 inches 2.59 inches 20.06 inches 4.47 inches

If the volume of a rectangular prism is V = x³ + 11x² + 36x + 36 and one has a side length of (x +6), what is the length of one of the other two sides? (x-2) (x-3) (x + 6) (x+3)

Alexandra and Maris are playing a game where they guess how many sides the regular polygon the other is holding has. Alexandra says her regular polygon has exactly 12 lines of symmetry. Maris says her regular polygon has an angle of rotational symmetry of 24°. How many sides does each regular polygon have?

Find the volume of a right circular cylinder with a radius of 2 ft and a height of 18 ft. (Note: Take the value of as 3.14.) Round your answer to the nearest thousandth, if necessary.

A company makes glass paperweights in the shape of a square pyramid. The base of the paperweight is three inches on one side, and it's four inches tall. What's the volume of one paperweight? A) 18 in³ B) 24 in ³ C) 12 in ³ D) 36 in ³

Identify the surface defined by the following equation. 10x - z² + y² = 0 The surface defined by the equation is an elliptic paraboloid. a hyperbolic paraboloid. an ellipsoid. a hyperboloid of two sheets. an elliptic cone. a cylinder. a hyperboloid of one sheet. a plane.

Let P be the plane passing through the point (1,2,-1) and perpendicular to the line of intersection of the planes 2x + z = 3 and 3y + 2z = 5 then equation of plane P is: 3x - 4y + 6z +11 = 0 3x-4y-6z-1=0 3x + 4y-6z-17 = 0 3x + 4y + 6z-5=0