Question

use the prism to complete problems 1–2.

1. how many faces does the prism have?

a. 8 b. 6 c. 12 d. 10

1. how many edges does the prism have?

a. 10 b. 16 c. 12 d. 18

1. to measure volume, you use meters.

circle: true or false

1. perpendicular lines form right angles. circle: true or false
2. are x = 4 and y = 8 solutions of the equation: y = x² - 2x + 1?

circle: yes or no

1. what type of lines are these?

circle: parallel or perpendicular

1. which fraction is equal to 0.125?

a. \\(\frac{1}{5}\\) b. \\(\frac{1}{4}\\) c. \\(\frac{1}{6}\\) d. \\(\frac{1}{8}\\)

1. 0° celsius = ______ ° fahrenheit
2. 1 gallon = ______ quarts
3. these lines form what type of an angle?

a. acute b. obtuse c. right

Explanation:

Problem 1

Step1: Identify the prism type

The prism shown is a hexagonal prism (has a hexagon as the base). A hexagonal prism has 2 hexagonal bases and 6 rectangular lateral faces.

Step2: Calculate the number of faces

Number of faces = number of bases + number of lateral faces = \(2 + 6 = 8\).

Step1: Recall the formula for edges of a prism

For a prism with an \(n\)-sided base, the number of edges \(E = 3n\). Here, the base is a hexagon (\(n = 6\)).

Step2: Calculate the number of edges

\(E = 3\times6 = 18\)? Wait, no, wait: Wait, a prism has 2 bases (each with \(n\) edges) and \(n\) lateral edges. So total edges: \(2n + n= 3n\). Wait, for a hexagonal prism, \(n = 6\), so \(3\times6 = 18\)? But wait, the options have 18 as option d. Wait, but let's check again. Wait, a hexagonal prism: each base is a hexagon (6 edges), so 2 bases: \(2\times6 = 12\) edges, and 6 lateral edges (connecting the corresponding vertices of the two bases). So total edges: \(12 + 6 = 18\). Yes.

Step1: Recall units of volume

Volume is measured in cubic units (e.g., cubic meters, \(m^3\)), while meters (\(m\)) is a unit of length.

Step2: Determine True/False

Since volume uses cubic meters, not meters (length unit), the statement is False.

Answer:

a. 8

Problem 2