Math Problem Statement

Use a two-dimensional model and the dimensions provided to calculate the circumference and area of the flower. Round to the nearest tenth, if necessary.

Solution

The problem asks to calculate the circumference and area of the flower based on its diameter of 5 inches.

  1. Circumference:

    • The formula for the circumference CC of a circle is: C=π×dC = \pi \times d where dd is the diameter. C=π×53.1416×5=15.7inchesC = \pi \times 5 \approx 3.1416 \times 5 = 15.7 \, \text{inches}
  2. Area:

    • The formula for the area AA of a circle is: A=π×r2A = \pi \times r^2 where rr is the radius, which is half the diameter. r=52=2.5inchesr = \frac{5}{2} = 2.5 \, \text{inches} A=π×(2.5)23.1416×6.25=19.6square inchesA = \pi \times (2.5)^2 \approx 3.1416 \times 6.25 = 19.6 \, \text{square inches}

So, the answers are:

  • Circumference: 15.7 inches
  • Area: 19.6 square inches

Would you like any more details on this calculation? Here are five follow-up questions to deepen understanding:

  1. What is the relationship between the radius and diameter of a circle?
  2. How does doubling the radius affect the area of a circle?
  3. Why do we use π\pi in circle-related calculations?
  4. How would the circumference change if the diameter doubled?
  5. Can you calculate the radius if only the circumference is given?

Tip: Always round your intermediate steps to avoid significant rounding errors in your final answer.

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Math Problem Analysis

Mathematical Concepts

Geometry
Circle

Formulas

Circumference of a circle: C = π × d
Area of a circle: A = π × r²

Theorems

Relationship between diameter and radius (r = d / 2)

Suitable Grade Level

Grades 6-8