Math Problem Statement

The circle shown has a radius of 5 inches. Which measurement is closest to the area in square inches of the circle? Use π = 3.14. A. 314 in² B. 78.5 in² C. 56.52 in² D. 28.26 in²

Solution

To solve the problem, we calculate the area of the circle using the formula:

A=πr2A = \pi r^2

Step-by-Step Solution:

  1. The radius of the circle is r=5r = 5 inches.
  2. Substitute π=3.14\pi = 3.14 and r=5r = 5 into the formula: A=3.14×(5)2A = 3.14 \times (5)^2
  3. Simplify: A=3.14×25=78.5in2A = 3.14 \times 25 = 78.5 \, \text{in}^2

The area of the circle is approximately 78.5 in².

Thus, the correct answer is B. 78.5 in².


Would you like additional details or have any questions?


Related Questions:

  1. What is the formula for the circumference of a circle, and how would you calculate it for this circle?
  2. If the diameter was given instead of the radius, how would you calculate the area?
  3. What would the area be if the radius was doubled?
  4. How does using a more precise value of π\pi (e.g., π3.14159\pi \approx 3.14159) affect the result?
  5. What are the practical applications of calculating the area of a circle in real-world scenarios?

Tip:

Always double-check the units and ensure you're squaring the radius properly when using the area formula!

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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

Grades 6-8