Math Problem Statement

Find the area and the circumference of a circle with diameter 8 yd. Use the value 3.14 for π, and do not round your answers.

Solution

The image contains a circle with a diameter of 8 yards, and the task is to find its area and circumference using π=3.14\pi = 3.14.

Given:

  • Diameter (dd) = 8 yards
  • Radius (rr) = d2=82=4\frac{d}{2} = \frac{8}{2} = 4 yards
  • π\pi = 3.14

Formulas:

  1. Area of a circle:
    Area=πr2\text{Area} = \pi r^2 Substituting values: Area=3.14×42=3.14×16=50.24 square yards\text{Area} = 3.14 \times 4^2 = 3.14 \times 16 = 50.24 \text{ square yards}

  2. Circumference of a circle:
    Circumference=πd\text{Circumference} = \pi d Substituting values: Circumference=3.14×8=25.12 yards\text{Circumference} = 3.14 \times 8 = 25.12 \text{ yards}

Final Answers:

  • Area = 50.24 square yards
  • Circumference = 25.12 yards

Would you like more details on these calculations or further questions? Here are five related questions:

  1. How would the area change if the diameter was doubled?
  2. What would the circumference be if the radius was 10 yards instead?
  3. How can you derive the radius if you're only given the circumference?
  4. What is the ratio of the circumference to the diameter of any circle?
  5. If the diameter was given in feet, how would you convert it to yards?

Tip: Always remember that the radius is half of the diameter, and most circle formulas are based on the radius.

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Math Problem Analysis

Mathematical Concepts

Geometry
Circle Properties

Formulas

Area of a circle: A = πr^2
Circumference of a circle: C = πd

Theorems

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Suitable Grade Level

Grades 6-8