Exploring Three-Dimensional Figures and Cross Sections

What is Euler's formula used to calculate in relation to polyhedra?

• The relationship between faces, vertices, and edges

• The volume of the polyhedron

• The surface area of each face

• The angle between edges

According to Euler's formula, if a polyhedron has 6 faces and 8 vertices, how many edges does it have?

• 16 edges

• 14 edges

• 10 edges

• 12 edges

What does the term 'vertices' refer to in geometry?

• The center points of faces

• The edges of a polyhedron

• The corners or points where edges meet

• The flat surfaces of a shape

In Euler's formula, if the number of faces and vertices added together equals 14, what is the sum of edges and 2?

• 12

• 14

• 16

• 10

If a polyhedron has 12 faces and 30 edges, how many vertices does it have?

• 20 vertices

• 24 vertices

• 22 vertices

• 18 vertices

What is a cross-section?

• A formula to calculate area

• A type of geometric transformation

• A 2D shape resulting from a cut through a 3D object

• A method to calculate volume

What shape is the cross-section when a plane slices through a pentagonal cone?

• Hexagon

• Pentagon

• Rectangle

• Triangle

How does a cross-section of an octahedron look when sliced through the top and bottom vertices?

• Circle

• Square

• Triangle

• Rhombus

What three-dimensional figure is formed when an isosceles triangle is rotated about its altitude?

• Cylinder

• Cone

• Sphere

• Cube

What is the result of rotating a polygon about an axis?

• No change

• A line

• A three-dimensional figure

• A new polygon