Cross Sections & 3D Solids Formed by Rotations

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​https://www.geogebra.org/m/c6vm6tub

Multiple Choice

An isosceles right triangle is placed on a coordinate grid. One of its legs is on the x-axis and the other on the y-axis. Which describes the shape created when the triangle is rotated about the 𝑥−𝑎𝑥𝑖𝑠?

• cone

• cylinder

• pyramid

• sphere

Multiple Choice

A rectangle will be rotated 360° about a line which contains the point of intersection of its diagonals and is parallel to a side. What three-dimensional shape will be created as a result of the rotation?

• cube

• rectangular prism

• cylinder

• sphere

Multiple Choice

Which of the following figures could be produced by translating a polygon back and forth in a direction perpendicular to the plane containing the figure?

• cone

• sphere

• cylinder

• prism

Multiple Choice

Which of the following is the best description for the resulting three-dimensional figure if a right triangle is rotated about the line containing its hypotenuse?

• a cone with slant height the same length as the longest leg

• a pyramid with triangular base

• two cones sharing the same circular base with apexes opposite each other

• a cone with slant height the same length as the shortest leg

Multiple Choice

William is drawing pictures of cross sections of the right circular cone as shown.

Which drawing cannot be a cross section of a cone?

Multiple Choice

Which figure can have the same cross section as a sphere?

Multiple Choice

If the rectangle below is continuously rotated about side w, which solid figure is formed?

• pyramid

• rectangular prism

• cone

• cylinder

Multiple Choice

What shape is the cross section formed by the intersection of a cone and a plane parallel to the base of the cone?

• circle

• trapezoid

• oval

• triangle

Multiple Choice

Andrea claims that any two cross sections of a cylinder that lie on parallel planes are congruent.

Is Andrea correct? If not, how can she modify her claim to be correct?

• No; any two cross sections of a cylinder that lie on planes parallel to the bases of the cylinder are congruent.

• No; any two cross sections of a cylinder that lie on planes parallel to a plane containing the axis of rotation are

  congruent.

• No; any two cross sections of a cylinder that lie on planes containing the axis of rotation are congruent.

• Andrea is correct.

Multiple Choice

Erin drew a three-dimensional figure with an intersecting plane to show a circular cross section. She then noticed that all cross sections parallel to the one she drew would also be circles. What additional information would allow you to conclude that Erin’s figure was a cylinder?

• The centers of the circular cross sections lie on a line.

• The circular cross sections are congruent.

• The circular cross sections are similar but not congruent.

• The figure also has at least one rectangular cross section.

Multiple Choice

A plane intersects a hexagonal prism. The plane is perpendicular to the base of the prism. Which two-dimensional figure is the cross section of the plane intersecting the prism?

• Triangle

• Trapezoid

• Hexagon

• Rectangle

Multiple Choice

A cross section of a right triangular prism is created by a plane cut through the points shown and is also perpendicular to the opposite base. What is the most specific name of the shape representing the cross section?

• Triangle

• Rectangle

• Trapezoid

• Parallelogram