Geometry | Unit 5 | Lesson 2: Slicing Solids | Practice Problems

Select all figures for which there exists a direction such that all cross sections taken at that direction are congruent.

• triangular pyramid

• square pyramid

• rectangular prism

• cube

• cone

Imagine an upright cone with its base resting on your horizontal desk. Sketch the cross section formed by intersecting a vertical plane not passing through the cone’s topmost point with the cone.

Imagine an upright cone with its base resting on your horizontal desk. Sketch the cross section formed by intersecting a horizontal plane with the cone.

Imagine an upright cone with its base resting on your horizontal desk. Sketch the cross section formed by intersecting a diagonal plane with the cone.

Name 2 figures for which a circle can be a cross section.

Sketch the solid of rotation formed by rotating the given two-dimensional figure using the dashed vertical line as an axis of rotation.

Draw a two-dimensional figure that could be rotated using a vertical axis of rotation to give the cone shown.

A regular hexagon and a regular octagon are both inscribed in the same circle. Which of these statements is true?

• The perimeter of the hexagon is less than the perimeter of the octagon, and each perimeter is less than the circumference of the circle.

• The perimeter of the octagon is less than the perimeter of the hexagon, and each perimeter is less than the circumference of the circle.

• The perimeter of the hexagon is greater than the perimeter of the octagon, and each perimeter is greater than the circumference of the circle.

• The perimeter of the octagon is greater than the perimeter of the hexagon, and each perimeter is greater than the circumference of the circle.

Technology required. Find the perimeter of the figure.

Match each trigonometric function to a ratio.