Cube A has a surface area of 18 cm². If the edge lengths of cube B are three times as long as the edge lengths of cube A, what is the surface area of cube B cube B cube A S.A. = 18 cm² S.A. = ? A. 486 cm? В. 162 cm? C. 54 cm?

Elementary Geometry For College Students, 7e
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Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
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ChapterP: Preliminary Concepts
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**Surface Area of Cubes – Example Problem**

**Problem Statement:**

Cube A has a surface area of \(18 \, \text{cm}^2\). If the edge lengths of cube B are three times as long as the edge lengths of cube A, what is the surface area of cube B?

![Cube Diagrams](cube-diagrams)

**Given Information:**

- **Cube A:**
    - Surface Area (S.A.) = \(18 \, \text{cm}^2\)

- **Cube B:**
    - Edge lengths are three times those of cube A.
    - Surface Area (S.A.) = ?

**Choices:**

A. \(486 \, \text{cm}^2\)

B. \(162 \, \text{cm}^2\)

C. \(54 \, \text{cm}^2\)

D. \(108 \, \text{cm}^2\)

### Explanation:

The surface area of a cube is given by \(6s^2\), where \(s\) is the length of one edge.

1. **Cube A:**
   \[
   6s^2 = 18 \, \text{cm}^2 \implies s^2 = 3 \, \text{cm}^2 \implies s = \sqrt{3} \, \text{cm}
   \]

2. **Cube B:**
   If the edge length of cube B is three times that of cube A, then:
   \[
   s_B = 3 \times s_A = 3 \times \sqrt{3} \, \text{cm}
   \]

   The surface area of cube B can be calculated as:
   \[
   S.A._{B} = 6 \times \left(3 \sqrt{3}\right)^2 = 6 \times 27 = 162 \, \text{cm}^2
   \]

Hence, the surface area of Cube B is \(162 \, \text{cm}^2 \) (Option B).
Transcribed Image Text:**Surface Area of Cubes – Example Problem** **Problem Statement:** Cube A has a surface area of \(18 \, \text{cm}^2\). If the edge lengths of cube B are three times as long as the edge lengths of cube A, what is the surface area of cube B? ![Cube Diagrams](cube-diagrams) **Given Information:** - **Cube A:** - Surface Area (S.A.) = \(18 \, \text{cm}^2\) - **Cube B:** - Edge lengths are three times those of cube A. - Surface Area (S.A.) = ? **Choices:** A. \(486 \, \text{cm}^2\) B. \(162 \, \text{cm}^2\) C. \(54 \, \text{cm}^2\) D. \(108 \, \text{cm}^2\) ### Explanation: The surface area of a cube is given by \(6s^2\), where \(s\) is the length of one edge. 1. **Cube A:** \[ 6s^2 = 18 \, \text{cm}^2 \implies s^2 = 3 \, \text{cm}^2 \implies s = \sqrt{3} \, \text{cm} \] 2. **Cube B:** If the edge length of cube B is three times that of cube A, then: \[ s_B = 3 \times s_A = 3 \times \sqrt{3} \, \text{cm} \] The surface area of cube B can be calculated as: \[ S.A._{B} = 6 \times \left(3 \sqrt{3}\right)^2 = 6 \times 27 = 162 \, \text{cm}^2 \] Hence, the surface area of Cube B is \(162 \, \text{cm}^2 \) (Option B).
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