https://file.aiquickdraw.com/mathbot/file/1726334155140fen02nb0.jpg

Let's analyze the areas of the ovals shown in the image, so we can rank them from the smallest to the largest.

### Areas provided:
1. **Oval I**: \( A = 3\pi \, \text{cm}^2 \)
2. **Oval II**: \( A = \frac{\sqrt{27}}{2} \, \text{cm}^2 \)
3. **Oval III**: \( A = 9.8 \, \text{cm}^2 \)
4. **Oval IV**: \( A = \frac{17}{3} \, \text{cm}^2 \)

### Converting areas:
1. **Oval I**: \( A = 3\pi \approx 3 \times 3.1416 = 9.4248 \, \text{cm}^2 \)
2. **Oval II**: \( A = \frac{\sqrt{27}}{2} = \frac{3\sqrt{3}}{2} \approx \frac{3 \times 1.732}{2} \approx \frac{5.196}{2} \approx 2.598 \, \text{cm}^2 \)
3. **Oval III**: \( A = 9.8 \, \text{cm}^2 \) (already in decimal form)
4. **Oval IV**: \( A = \frac{17}{3} \approx 5.6667 \, \text{cm}^2 \)

### Ranking the areas from least to greatest:
- **Oval II**: \( 2.598 \, \text{cm}^2 \)
- **Oval IV**: \( 5.6667 \, \text{cm}^2 \)
- **Oval I**: \( 9.4248 \, \text{cm}^2 \)
- **Oval III**: \( 9.8 \, \text{cm}^2 \)

So, the correct order from least to greatest area is:
- **Oval II, Oval IV, Oval I, Oval III**

This corresponds to **option A**.

Would you like further details on this or have any other questions?

### Related questions:
1. What is the general formula for the area of an ellipse (oval)?
2. How is \( \pi \) approximated in calculations?
3. How does the square root of a number affect the value in equations?
4. What are different ways to express an area in terms of units?
5. How can we approximate irrational numbers in calculations?

#### Tip:
When calculating areas or other values involving \( \pi \), it is common to use \( 3.1416 \) or \( \frac{22}{7} \) for easier calculations.

The area of four ovals are shown below. Which list shows the ovals in order from least to the greatest area?

Compare the areas of four ovals, calculated using decimal and approximation methods. This problem covers core mathematical concepts like area calculation, square roots, and approximations, suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation