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?
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
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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Question
**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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb602927-d5c2-4b17-99bc-cf43c066f5a5%2Fb0f8c505-e95e-4f93-80d1-e1b3d9f30801%2Fmbtmtu_processed.png&w=3840&q=75)
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?
**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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