Answered

Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

A company makes different-sized shoeboxes in the shape of rectangular prisms. Match the area of the material needed to make each box to the box's dimensions.

1. 10 in [tex]$\times$[/tex] 6 in [tex]$\times$[/tex] 6 in
2. 14 in [tex]$\times$[/tex] 5 in [tex]$\times$[/tex] 5 in
3. 16 in [tex]$\times$[/tex] 6 in [tex]$\times$[/tex] 4 in
4. 12 in [tex]$\times$[/tex] 5 in [tex]$\times$[/tex] 6 in

A. [tex]$324 \text{ in}^2$[/tex]
B. [tex]$368 \text{ in}^2$[/tex]
C. [tex]$312 \text{ in}^2$[/tex]
D. [tex]$330 \text{ in}^2$[/tex]

Sagot :

GinnyAnswer
To match the given surface areas of the shoeboxes to their respective dimensions, let's calculate the surface area for each box first. The formula for the surface area of a rectangular prism is as follows:

[tex]\[ \text{Surface Area} = 2(l \times w + l \times h + w \times h) \][/tex]

Where \( l \) is the length, \( w \) is the width, and \( h \) is the height of the box.

### Calculations:

1. Dimensions: 10 in × 6 in × 6 in
[tex]\[ \text{Surface Area} = 2(10 \times 6 + 10 \times 6 + 6 \times 6) \][/tex]
[tex]\[ \text{Surface Area} = 2(60 + 60 + 36) \][/tex]
[tex]\[ \text{Surface Area} = 2 \times 156 \][/tex]
[tex]\[ \text{Surface Area} = 312 \, \text{in}^2\][/tex]

2. Dimensions: 14 in × 5 in × 5 in
[tex]\[ \text{Surface Area} = 2(14 \times 5 + 14 \times 5 + 5 \times 5) \][/tex]
[tex]\[ \text{Surface Area} = 2(70 + 70 + 25) \][/tex]
[tex]\[ \text{Surface Area} = 2 \times 165 \][/tex]
[tex]\[ \text{Surface Area} = 330 \, \text{in}^2\][/tex]

3. Dimensions: 16 in × 6 in × 4 in
[tex]\[ \text{Surface Area} = 2(16 \times 6 + 16 \times 4 + 6 \times 4) \][/tex]
[tex]\[ \text{Surface Area} = 2(96 + 64 + 24) \][/tex]
[tex]\[ \text{Surface Area} = 2 \times 184 \][/tex]
[tex]\[ \text{Surface Area} = 368 \, \text{in}^2\][/tex]

4. Dimensions: 12 in × 5 in × 6 in
[tex]\[ \text{Surface Area} = 2(12 \times 5 + 12 \times 6 + 5 \times 6) \][/tex]
[tex]\[ \text{Surface Area} = 2(60 + 72 + 30) \][/tex]
[tex]\[ \text{Surface Area} = 2 \times 162 \][/tex]
[tex]\[ \text{Surface Area} = 324 \, \text{in}^2\][/tex]

### Matching Results:

- The box with dimensions 10 in × 6 in × 6 in has a surface area of 312 in².
- The box with dimensions 14 in × 5 in × 5 in has a surface area of 330 in².
- The box with dimensions 16 in × 6 in × 4 in has a surface area of 368 in².
- The box with dimensions 12 in × 5 in × 6 in has a surface area of 324 in².

So, the matches are:
- \( 312 \, \text{in}^2 \) matches with \( 10 \, \text{in} \times 6 \, \text{in} \times 6 \, \text{in} \)
- \( 330 \, \text{in}^2 \) matches with \( 14 \, \text{in} \times 5 \, \text{in} \times 5 \, \text{in} \)
- \( 368 \, \text{in}^2 \) matches with \( 16 \, \text{in} \times 6 \, \text{in} \times 4 \, \text{in} \)
- [tex]\( 324 \, \text{in}^2 \)[/tex] matches with [tex]\( 12 \, \text{in} \times 5 \, \text{in} \times 6 \, \text{in} \)[/tex]
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.