### Cereal Box Design ChallengeA cereal company wants to change the shape of its cereal box to attract the attention of shoppers. The original cereal box has dimensions of 8 inches x 3 inches x 11 inches. The new box the cereal company is considering would have dimensions of 10 inches x 10 inches x 3 inches.#### A. Volume Comparison**Question:** Which box holds more cereal? Show your work and explain your solution.**Solution:**To determine which box holds more cereal, we need to calculate the volume of each box.**Original Box:**- Dimensions: 8 in x 3 in x 11 in- Volume = Length x Width x Height- Volume = 8 in x 3 in x 11 in = 264 cubic inches**New Box:**- Dimensions: 10 in x 10 in x 3 in- Volume = Length x Width x Height- Volume = 10 in x 10 in x 3 in = 300 cubic inches**Conclusion:**The new box holds more cereal since 300 cubic inches > 264 cubic inches.#### B. Surface Area Comparison**Question:** Which box requires more material to make? Show your work and explain your solution.**Solution:**To determine which box requires more material to make, we need to calculate the surface area of each box.**Original Box:**- Length = 8 in, Width = 3 in, Height = 11 in- Surface Area = 2(lw + lh + wh)- Surface Area = 2(8 in x 3 in + 8 in x 11 in + 3 in x 11 in)- Surface Area = 2(24 in² + 88 in² + 33 in²)- Surface Area = 2(145 in²)- Surface Area = 290 square inches**New Box:**- Length = 10 in, Width = 10 in, Height = 3 in- Surface Area = 2(lw + lh + wh)- Surface Area = 2(10 in x 10 in + 10 in x 3 in + 10 in x 3 in)- Surface Area = 2(100 in² + 30 in² + 30 in²)- Surface Area = 2(160 in²)- Surface Area = 320 square inches

Answered: Image /qna-images/answer/2644c1c7-8554-4a2d-89a7-11b0d39191a7.jpg

A cereal company wants to change the shape of its cereal box in order to attract the attention of shoppers. The original cereal box has dimensions of 8 inches x 3 inches x new box the cereal company is thinking of would have dimensions of x 3 inches. 11 inches. The 10 inches x 10 inches A. Which box holds more cereal? Show your work and explain your solution.

A cereal company wants to change the shape of its cereal box in order to attract the attention of shoppers. The original cereal box has dimensions of 8 inches x 3 inches x new box the cereal company is thinking of would have dimensions of x 3 inches. 11 inches. The 10 inches x 10 inches A. Which box holds more cereal? Show your work and explain your solution.

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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### Cereal Box Design Challenge

A cereal company wants to change the shape of its cereal box to attract the attention of shoppers. The original cereal box has dimensions of 8 inches x 3 inches x 11 inches. The new box the cereal company is considering would have dimensions of 10 inches x 10 inches x 3 inches.

#### A. Volume Comparison
**Question:** Which box holds more cereal? Show your work and explain your solution.

**Solution:**
To determine which box holds more cereal, we need to calculate the volume of each box.

**Original Box:**
- Dimensions: 8 in x 3 in x 11 in
- Volume = Length x Width x Height
- Volume = 8 in x 3 in x 11 in = 264 cubic inches

**New Box:**
- Dimensions: 10 in x 10 in x 3 in
- Volume = Length x Width x Height
- Volume = 10 in x 10 in x 3 in = 300 cubic inches

**Conclusion:**
The new box holds more cereal since 300 cubic inches > 264 cubic inches.

#### B. Surface Area Comparison
**Question:** Which box requires more material to make? Show your work and explain your solution.

**Solution:**
To determine which box requires more material to make, we need to calculate the surface area of each box.

**Original Box:**
- Length = 8 in, Width = 3 in, Height = 11 in
- Surface Area = 2(lw + lh + wh)
- Surface Area = 2(8 in x 3 in + 8 in x 11 in + 3 in x 11 in)
- Surface Area = 2(24 in² + 88 in² + 33 in²)
- Surface Area = 2(145 in²)
- Surface Area = 290 square inches

**New Box:**
- Length = 10 in, Width = 10 in, Height = 3 in
- Surface Area = 2(lw + lh + wh)
- Surface Area = 2(10 in x 10 in + 10 in x 3 in + 10 in x 3 in)
- Surface Area = 2(100 in² + 30 in² + 30 in²)
- Surface Area = 2(160 in²)
- Surface Area = 320 square inches

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