THREE-DIMENSIONAL FIGURES WORKSHEET

Question 1 :

What is the relationship between the numbers of vertices V, edges E, and faces F of a polyhedron ? 

Question 2 :

List the numbers of vertices, edges, and faces of each Platonic solid.

Question 3 : 

Tell whether each solid is a polyhedron. If it is, name the polyhedron.

Question 4 : 

Describe the shape formed by the intersection of the plane and the solid.

Question 5 : 

Sketch the solid produced by rotating the figure around the given axis. Then identify and describe the solid.

Question 6 : 

Give an example and list the properties for each of the following prisms/pyramids. 

Triangular Prism

Rectangular Prism

Cube

Square Pyramid

Triangular Pyramid

Question 7 : 

Give an example and list the properties for each of the following figures with curved faces.

Cylinder

Cone

Sphere

Question 1 :

What is the relationship between the numbers of vertices V, edges E, and faces F of a polyhedron ? 

Answer :

A polyhedron is a solid that is bounded by polygons, called faces.

• Each vertex is a point.

• Each edge is a segment of a line.

• Each face is a portion of a plane.

Question 2 :

List the numbers of vertices, edges, and faces of each Platonic solid.

Answer :

Question 3 : 

Tell whether each solid is a polyhedron. If it is, name the polyhedron.

Answer : 

(a)  The solid is formed by polygons, so it is a polyhedron. The two bases are congruent rectangles, so it is a rectangular prism.

(b)  The solid is formed by polygons, so it is a polyhedron. The base is a hexagon, so it is a hexagonal pyramid.

(c) The cone has a curved surface, so it is not a polyhedron.

Question 4 : 

Describe the shape formed by the intersection of the plane and the solid.

Answer : 

(a)  The cross section is a hexagon.

(b)  The cross section is a triangle.

(c)  The cross section is a rectangle.

(d)  The cross section is a circle.

(e)  The cross section is a circle.

(f) The cross section is a trapezoid.

Question 5 : 

Sketch the solid produced by rotating the figure around the given axis. Then identify and describe the solid.

Answer : 

(a) The solid is a cylinder with a height of 9 and a base radius of 4.

(b) The solid is a cone with a height of 5 and a base radius of 2.

Question 6 : 

Give an example and list the properties for each of the following prisms/pyramids. 

Triangular Prism

Rectangular Prism

Cube

Square Pyramid

Triangular Pyramid

Answer : 

Question 7 : 

Give an example and list the properties for each of the following figures with curved faces.

Cylinder

Cone

Sphere

Answer : 

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