Reference no: EM131613247
Question 1 A regular pyramid with a square base is cut by two planes: one parallel to the base and one perpendicular to the base and through the center. What are the cross sections produced?
Question 2
If the volumes of both solids are the same, which of the following corresponds to the value of a: the side length of the base of the square prism?
2
4
√(2Π)
4√Π
Question 3
Given the following two solids.
Complete the following prompts using complete sentences.
a. Write a hypothesis that compares the volumes of both figures.
b. Calculate the volume of each prism. Was your hypothesis correct? Why or why not?
Question 4
The prism is cut by a plane that is parallel to a base of the prism.
The intersection of the prism and the plane is a cross section.
Question 5
Given the intersection of a pyramid and a plane with a trapezoidal cross section. Which option is true about the plane of intersection?
The pyramid is cut with a plane parallel to the base.
The pyramid is cut with a plane passing through the top vertex and perpendicular to the base. The pyramid is cut with a plane perpendicular to the base, but not through the top vertex.
The pyramid is cut with a plane passing through the top vertex and not perpendicular to the base.
Question 6
The intersection of a right cylinder and a plane makes an oval cross section. Which option is true about the plane of intersection?
The right cylinder is cut with a plane parallel to the base.
The right cylinder is cut with a plane perpendicular to the base and passing through the center.
The right cylinder is cut with a plane perpendicular to the base but not passing through the center.
The right cylinder is cut with a plane that is neither parallel nor perpendicular to the base.
Question 7
A plane which passes through three edges of a cube produces a triangular cross section as shown.
In two or more complete sentences, explain how the plane should pass through the cube in order to produce a cross section that is a regular hexagon.
Question 8
A horizontal plane passes through a cone that has a horizontal base. Which figure or figures can be produced? Select all that apply.
point
triangle
circle
line segment
trapezoid
rectangle
Question 9
A vertical plane passes through a pyramid that has a horizontal base.
Which of the following can be produced from the intersection of the vertical plane and pyramid? Select all that apply.
square
triangle
circle
horizontal line segment
trapezoid
rectangle
Question 10
Which three-dimensional shapes do not have identical cross sections when cut by planes that are parallel to the base? Select all that apply
cone
rectangular pyramid
Question 11
a. Draw a picture of the three-dimensional shape that is produced when the circle is rotated about the y-axis.
b. In two or more complete sentences, describe the three-dimensional shape.
Question 12
A potter is creating a design for a red-colored urn. He starts with the design shown on the coordinate grid.
The design is rotated about the line x = 1 to produce the shape of the urn. Finish the potter's design by drawing a picture of what the urn looks like. In your picture, include a properly labeled coordinate plane and the line x = 1.
Use the upload option to submit your drawing.
Question 13
A right triangle is rotated around a line that includes one of the legs of the triangle.
What figure is created?
a pyramid
a cone
a larger triangle
a diamond
two cones sharing a base