Math Problem Statement

Find the area and the circumference of a circle with radius 3 ft. Use the value 3.14 for π, and do not round your answers. Be sure to include the correct units in your answers.

Solution

Let’s solve the problem step by step.

Given:

  • Radius of the circle (rr) = 3 ft
  • Approximation for π\pi: π=3.14\pi = 3.14

Formulas:

  1. Area of a circle: Area=πr2\text{Area} = \pi r^2

  2. Circumference of a circle: Circumference=2πr\text{Circumference} = 2\pi r

Calculation:

1. Area:

Area=3.14×(3)2\text{Area} = 3.14 \times (3)^2 Area=3.14×9=28.26ft2\text{Area} = 3.14 \times 9 = 28.26 \, \text{ft}^2

2. Circumference:

Circumference=2×3.14×3\text{Circumference} = 2 \times 3.14 \times 3 Circumference=18.84ft\text{Circumference} = 18.84 \, \text{ft}

Final Answers:

  • Area: 28.26ft228.26 \, \text{ft}^2
  • Circumference: 18.84ft18.84 \, \text{ft}

Would you like a more detailed explanation of the steps? Let me know!


Related Questions:

  1. What is the formula for the area and circumference of a semicircle?
  2. How would the answers change if the radius were doubled?
  3. Why is π\pi important in circular geometry?
  4. How can you calculate the diameter from the circumference?
  5. What is the difference between exact values and approximations in geometry?

Tip:

Always ensure the units in your answers match the context of the problem to avoid confusion!

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Math Problem Analysis

Mathematical Concepts

Geometry
Circles

Formulas

Area of a circle: πr^2
Circumference of a circle: 2πr

Theorems

Properties of a circle

Suitable Grade Level

Grades 6-8