Math Problem Statement

A group of Tibetan monks created a sand mandala at an art museum. The mandala was in the shape of a circle with a radius of 2.5 ft. What was the area of the sand mandala? Use 3.14 for π.

Solution

To find the area of the sand mandala in the shape of a circle with a radius of 2.5 feet, we can use the formula for the area of a circle:

A=πr2A = \pi r^2

Given:

  • Radius (rr) = 2.5 feet
  • π3.14\pi \approx 3.14

Calculation:

A=3.14(2.5)2A = 3.14 \cdot (2.5)^2 A=3.146.25A = 3.14 \cdot 6.25 A=19.625ft2A = 19.625 \, \text{ft}^2

Final Answer:

The area of the sand mandala is 19.63 ft² (rounded to two decimal places).

Let me know if you'd like further details or explanations. Here are some related questions for practice:

  1. What is the circumference of the same circle using C=2πrC = 2 \pi r?
  2. How would the area change if the radius doubled?
  3. Can you calculate the diameter of the circle?
  4. If the area was calculated using π3.1416\pi \approx 3.1416, what would be the result?
  5. How would the formula change for a semicircular sand mandala?

Tip: Always square the radius before multiplying by π\pi when calculating the area of a circle.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area of a Circle

Formulas

A = πr²

Theorems

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Suitable Grade Level

Grade 7