Math Problem Statement

Find the circumference and area of the adjacent circle. 7.3 m Question content area bottom Part 1 The circumference of the circle is approximately

22.9 m. ​(Type an integer or decimal rounded to the nearest tenth as​ needed.) Part 2 The area of the circle is approximately

enter your response here m squared . ​(Type an integer or decimal rounded to the nearest tenth as​ needed.)

Solution

To solve this, let's use the formulas for the circumference and area of a circle.

Given:

  • Radius r=7.3mr = 7.3 \, \text{m}

Part 1: Circumference

The formula for the circumference of a circle is: C=2πrC = 2 \pi r Substitute r=7.3r = 7.3: C=2×π×7.345.9mC = 2 \times \pi \times 7.3 \approx 45.9 \, \text{m}

Part 2: Area

The formula for the area of a circle is: A=πr2A = \pi r^2 Substitute r=7.3r = 7.3: A=π×(7.3)2167.4m2A = \pi \times (7.3)^2 \approx 167.4 \, \text{m}^2

Final Answers

  1. Circumference: 45.9m\approx 45.9 \, \text{m}
  2. Area: 167.4m2\approx 167.4 \, \text{m}^2

Would you like more details, or have any questions?

Here are five related questions to extend understanding:

  1. What would the area be if the radius was doubled?
  2. How does changing the radius affect the circumference?
  3. Can you derive the formulas for circumference and area from first principles?
  4. How would the formulas change if this were a semicircle?
  5. What is the area-to-circumference ratio, and what does it signify?

Tip: Always use π3.1416\pi \approx 3.1416 or the π\pi button on a calculator for more accurate results.

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Math Problem Analysis

Mathematical Concepts

Geometry
Circle Properties

Formulas

Circumference of a circle: C = 2πr
Area of a circle: A = πr²

Theorems

Definition of a Circle
Properties of π (Pi)

Suitable Grade Level

Grades 6-8