Math Problem Statement

How much trim is needed to surround two circular gardens that each have a diameter of 13 feet? Use 3.14 for pi.

Solution

To determine how much trim is needed to surround two circular gardens, we need to find the circumference of each garden and then multiply by 2 for the total amount of trim.

The formula for the circumference of a circle is:

C=π×dC = \pi \times d

where CC is the circumference and dd is the diameter of the circle.

Given:

  • Diameter d=13feetd = 13 \, \text{feet}
  • π=3.14\pi = 3.14

Now, calculate the circumference for one garden:

C=3.14×13=40.82feetC = 3.14 \times 13 = 40.82 \, \text{feet}

Since there are two gardens, multiply by 2:

Total trim=40.82×2=81.64feet\text{Total trim} = 40.82 \times 2 = 81.64 \, \text{feet}

Thus, 81.64 feet of trim is needed to surround both gardens.

Would you like more details or have any questions?

Here are five related questions for further exploration:

  1. What is the area of each circular garden?
  2. How would the amount of trim change if the diameter was 15 feet instead?
  3. How much trim would be required for three circular gardens of the same size?
  4. What would the trim length be for a garden with a diameter of 20 feet?
  5. What is the relationship between the diameter and circumference of a circle?

Tip: For larger calculations, rounding π\pi to 3.1416 provides a more accurate result.

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Math Problem Analysis

Mathematical Concepts

Geometry
Circumference of a Circle
Multiplication

Formulas

Circumference formula: C = π × d

Theorems

Relationship between diameter and circumference: C = πd

Suitable Grade Level

Grades 6-8