An artist painted a 1 foot square painting. Now she wants to create more paintings of different sizes that are all scaled copies of her original painting. The paint she uses is expensive, so she wants to know the sizes she can create using different amounts of paint. 1. Suppose the artist has enough paint to cover 9 square feet. If she uses all her paint, by what scale factor can she dilate her original painting? 2. Complete the table that shows the relationship between the dilated area () and the scale factor (x). Round values to the nearest tenth if needed. Use the applet at the end of the lesson to help, if you choose. Dilations dilated area in sq ft. 0 1 4 9 16 3. On graph paper, plot the points from the table and connect them with a smooth curve. 4. Use your graph to estimate the scale factor the artist could use if she had enough paint to cover 12 square feet. paint to 5. Suppose the painter has enough paint to cover 1 square foot, and she scale factor she can use? scale factor (k) additional 2 square feet. How does this change the 6. Suppose the painter has enough paint to cover 14 square feet, and she buys enough paint to cover an additional 2 square feet. How does this change the scale factor she can use?

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter10: Measurement, Area, And Volume
Section10.8: Volumes Of Pyramids And Cones
Problem 16E
Question
**Title: Exploring Scale Factors in Art**

**Introduction:**
An artist painted a 1-foot square painting. Now she wants to create more paintings of different sizes that are all scaled copies of her original painting. The paint she uses is expensive, so she wants to know the sizes she can create using different amounts of paint.

**Instructions:**

1. **Determine Scale Factor for 9 Square Feet:**
   - Suppose the artist has enough paint to cover 9 square feet. If she uses all her paint, by what scale factor can she dilate her original painting?

2. **Complete the Dilation Table:**
   - Fill in the table to show the relationship between the dilated area and the scale factor (\(k\)). Round values to the nearest tenth if needed.

| Dilated Area (sq ft) | Scale Factor (\(k\)) |
|----------------------|----------------------|
| 0                    |                      |
| 1                    |                      |
| 4                    |                      |
| 9                    |                      |
| 16                   |                      |

3. **Graph the Points:**
   - On graph paper, plot the points from the table and connect them with a smooth curve.

4. **Estimate Scale Factor for 12 Square Feet:**
   - Use your graph to estimate the scale factor the artist could use if she had enough paint to cover 12 square feet.

5. **Additional Paint Calculation for 1 Square Foot:**
   - Suppose the painter has enough paint to cover 1 square foot, and she buys enough paint to cover an additional 2 square feet. How does this change the scale factor she can use?

6. **Additional Paint Calculation for 14 Square Feet:**
   - Suppose the painter has enough paint to cover 14 square feet, and she buys enough paint to cover an additional 2 square feet. How does this change the scale factor she can use?

**Conclusion:**
Understanding the relationship between dilated area and scale factors helps in resource management and planning in art projects. Use these calculations and graphs to explore creative possibilities efficiently.
Transcribed Image Text:**Title: Exploring Scale Factors in Art** **Introduction:** An artist painted a 1-foot square painting. Now she wants to create more paintings of different sizes that are all scaled copies of her original painting. The paint she uses is expensive, so she wants to know the sizes she can create using different amounts of paint. **Instructions:** 1. **Determine Scale Factor for 9 Square Feet:** - Suppose the artist has enough paint to cover 9 square feet. If she uses all her paint, by what scale factor can she dilate her original painting? 2. **Complete the Dilation Table:** - Fill in the table to show the relationship between the dilated area and the scale factor (\(k\)). Round values to the nearest tenth if needed. | Dilated Area (sq ft) | Scale Factor (\(k\)) | |----------------------|----------------------| | 0 | | | 1 | | | 4 | | | 9 | | | 16 | | 3. **Graph the Points:** - On graph paper, plot the points from the table and connect them with a smooth curve. 4. **Estimate Scale Factor for 12 Square Feet:** - Use your graph to estimate the scale factor the artist could use if she had enough paint to cover 12 square feet. 5. **Additional Paint Calculation for 1 Square Foot:** - Suppose the painter has enough paint to cover 1 square foot, and she buys enough paint to cover an additional 2 square feet. How does this change the scale factor she can use? 6. **Additional Paint Calculation for 14 Square Feet:** - Suppose the painter has enough paint to cover 14 square feet, and she buys enough paint to cover an additional 2 square feet. How does this change the scale factor she can use? **Conclusion:** Understanding the relationship between dilated area and scale factors helps in resource management and planning in art projects. Use these calculations and graphs to explore creative possibilities efficiently.
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