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4 6. 12 16 6. 4 72 528

4 6. 12 16 6. 4 72 528

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Use the rectangular prism to complete the table . Only 4-8 on the table is what I need assistance with please.

**Understanding Rectangular Prisms: Completing Tables and Calculations** Rectangular prisms are three-dimensional figures with six faces, all of which are rectangles. The characteristics of a rectangular prism can be described using three dimensions: length (l), width (w), and height (h). The image provides an illustration of a rectangular prism and a table with four columns for different sets of dimensions and corresponding measurements such as Lateral Area, Surface Area, and Volume. ### Example Table of a Rectangular Prism Column definitions: 1. **Length (l)**: The measurement of the prism's longer side. 2. **Width (w)**: The measurement of the prism's shorter side (base). 3. **Height (h)**: The measurement from the base to the top of the prism. Note: Some values in the table are obscured. #### Table illustrating given and derived measurements: | | 1 | 2 | 3 | 4 | |----------------|----|----|----|----| | **Length** | 8 | 12 | 6 | 12 | | **Width** | 3 | 5 | | 6 | | **Height** | 4 | | 2 | 2 | | **Lateral Area** | | | | | | **Surface Area** | | | | | | **Volume** | | | | 48 | #### Formulas Needed for Calculations: 1. **Lateral Surface Area (LSA)**: \[ LSA = 2h(l + w) \] where \( l \), \( w \), and \( h \) are the length, width, and height of the rectangular prism, respectively. 2. **Surface Area (SA)**: \[ SA = 2(lw + lh + wh) \] where \( l \), \( w \), and \( h \) are the length, width, and height of the rectangular prism, respectively. 3. **Volume (V)**: \[ V = l \times w \times h \] where \( l \), \( w \), and \( h \) are the length, width, and height of the rectangular prism, respectively. ### Applying Form
Transcribed Image Text:**Understanding Rectangular Prisms: Completing Tables and Calculations** Rectangular prisms are three-dimensional figures with six faces, all of which are rectangles. The characteristics of a rectangular prism can be described using three dimensions: length (l), width (w), and height (h). The image provides an illustration of a rectangular prism and a table with four columns for different sets of dimensions and corresponding measurements such as Lateral Area, Surface Area, and Volume. ### Example Table of a Rectangular Prism Column definitions: 1. **Length (l)**: The measurement of the prism's longer side. 2. **Width (w)**: The measurement of the prism's shorter side (base). 3. **Height (h)**: The measurement from the base to the top of the prism. Note: Some values in the table are obscured. #### Table illustrating given and derived measurements: | | 1 | 2 | 3 | 4 | |----------------|----|----|----|----| | **Length** | 8 | 12 | 6 | 12 | | **Width** | 3 | 5 | | 6 | | **Height** | 4 | | 2 | 2 | | **Lateral Area** | | | | | | **Surface Area** | | | | | | **Volume** | | | | 48 | #### Formulas Needed for Calculations: 1. **Lateral Surface Area (LSA)**: \[ LSA = 2h(l + w) \] where \( l \), \( w \), and \( h \) are the length, width, and height of the rectangular prism, respectively. 2. **Surface Area (SA)**: \[ SA = 2(lw + lh + wh) \] where \( l \), \( w \), and \( h \) are the length, width, and height of the rectangular prism, respectively. 3. **Volume (V)**: \[ V = l \times w \times h \] where \( l \), \( w \), and \( h \) are the length, width, and height of the rectangular prism, respectively. ### Applying Form
**Multiplication Table with Missing Values** This image presents a partially filled multiplication table. Each cell displays the product of the values at the corresponding row and column. ### Table Structure and Contents: | | | | | | | |---|---|---|---|---|---| | | **4** | **5** | **6** | **7** | **8** | | **3** | 12 | | 18 | | 3 | | **2** | 6 | 9 | | | 2 | | **1** | | 5 | 4 | 4 | | | **9** | 72 | | | 208 | | | **10** | | 528 | | | 22 | | **50** | | | 450 | | | ### Explanation: - **Row Headers and Column Headers:** - The row headers represent the multiplicands (3, 2, 1, 9, 10, 50). - The column headers represent the multipliers (4, 5, 6, 7, 8). - **Filled Values:** - The products of the row headers (multiplicands) and column headers (multipliers) are provided. - Some cells are filled based on the multiplication of corresponding headers. - **Missing Values:** - Blanks indicate where the products are missing. These can be computed based on the row and column headers. ### Interpreting the Table: To find the missing values, multiply the row header by the column header. For example: - The cell in the second row and fourth column would be \(3 \times 6 = 18\). - Similarly, for the cell in the fifth row and first column, the value is missing; hence it should be \(9 \times 4 = 36\). This table helps students practice multiplication and understand the relationships between different numbers. Fill in the blanks to complete the table and verify your multiplications!
Transcribed Image Text:**Multiplication Table with Missing Values** This image presents a partially filled multiplication table. Each cell displays the product of the values at the corresponding row and column. ### Table Structure and Contents: | | | | | | | |---|---|---|---|---|---| | | **4** | **5** | **6** | **7** | **8** | | **3** | 12 | | 18 | | 3 | | **2** | 6 | 9 | | | 2 | | **1** | | 5 | 4 | 4 | | | **9** | 72 | | | 208 | | | **10** | | 528 | | | 22 | | **50** | | | 450 | | | ### Explanation: - **Row Headers and Column Headers:** - The row headers represent the multiplicands (3, 2, 1, 9, 10, 50). - The column headers represent the multipliers (4, 5, 6, 7, 8). - **Filled Values:** - The products of the row headers (multiplicands) and column headers (multipliers) are provided. - Some cells are filled based on the multiplication of corresponding headers. - **Missing Values:** - Blanks indicate where the products are missing. These can be computed based on the row and column headers. ### Interpreting the Table: To find the missing values, multiply the row header by the column header. For example: - The cell in the second row and fourth column would be \(3 \times 6 = 18\). - Similarly, for the cell in the fifth row and first column, the value is missing; hence it should be \(9 \times 4 = 36\). This table helps students practice multiplication and understand the relationships between different numbers. Fill in the blanks to complete the table and verify your multiplications!
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