Math Problem Statement

Find the circumference and area of the adjacent circle. Use the pi key for pi. 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. m squared . ​(Type an integer or decimal rounded to the nearest tenth as​ needed.)

Solution

To solve for both the circumference and the area of a circle, we can use the formulas below:

  1. Circumference: C=2πrC = 2 \pi r
  2. Area: A=πr2A = \pi r^2

where rr is the radius of the circle.

Given:

  • Radius (rr) = 7.3 meters

Part 1: Circumference

C=2π×7.3C = 2 \pi \times 7.3 C2×3.14159×7.345.9 metersC \approx 2 \times 3.14159 \times 7.3 \approx 45.9 \text{ meters}

The circumference, rounded to the nearest tenth, is approximately 45.9 meters.

Part 2: Area

A=π×(7.3)2A = \pi \times (7.3)^2 A3.14159×53.29167.4 square metersA \approx 3.14159 \times 53.29 \approx 167.4 \text{ square meters}

The area, rounded to the nearest tenth, is approximately 167.4 square meters.


Would you like further explanation on these calculations, or have any specific questions?

Here are five related questions to deepen your understanding:

  1. How would the area and circumference change if the radius doubled?
  2. Can you calculate the diameter of the circle and use it to find the circumference?
  3. What is the formula for the area of a sector if only a portion of the circle is given?
  4. How does rounding to different decimal places affect the precision of circumference and area?
  5. Can you express the circumference and area in terms of a fraction of π\pi for exact values?

Tip: Remember that for circular calculations, keeping a few more decimal places in π\pi can help maintain precision in intermediate steps before rounding the final answer.

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Math Problem Analysis

Mathematical Concepts

Geometry
Circles
Measurement of Circumference and Area

Formulas

Circumference = 2πr
Area = πr^2

Theorems

Properties of circles
Area and circumference relationships

Suitable Grade Level

Grades 6-8