Question

unit 1 lesson 13 cumulative practice problems

1. select all the polyhedra.

a
b
c
d
e
a. a
b. b
c. c
d. d
e. e

1. a. is this polyhedron a prism, a pyramid, or neither? explain how you know.

b. how many faces, edges, and vertices does it have?

Explanation:

Step1: Recall polyhedron definition

A polyhedron is a three - dimensional solid made up of flat polygonal faces, straight edges and sharp vertices.

Step2: Analyze option A

It is a pyramid with flat triangular and polygonal faces, straight edges and vertices. So it is a polyhedron.

Step3: Analyze option B

It is a polyhedron with flat polygonal faces, straight edges and vertices.

Step4: Analyze option C

A cone has a curved surface, so it is not a polyhedron.

Step5: Analyze option D

It is a prism with flat polygonal faces, straight edges and vertices. So it is a polyhedron.

Step6: Analyze option E

A sphere has a curved surface, so it is not a polyhedron.

for question 2a:

Step1: Recall prism and pyramid definitions

A prism has two congruent and parallel bases, and the lateral faces are parallelograms. A pyramid has one base and triangular lateral faces that meet at a single vertex.

Step2: Analyze the given polyhedron

The given polyhedron has two congruent and parallel octagonal bases, and the lateral faces are rectangles (a type of parallelogram). So it is a prism.

for question 2b:

Step1: Count faces

The two octagonal bases and 8 rectangular lateral faces make a total of 10 faces.

Step2: Count edges

Each octagonal base has 8 edges, and there are 8 vertical edges connecting the bases. So there are \(8\times2 + 8=24\) edges.

Step3: Count vertices

Each octagonal base has 8 vertices, so there are 16 vertices.

Answer:

A. A
B. B
D. D