Math Problem Statement

what is the area of this circle? When calculating use 3.14 as the estimation of pi. round to one decimal place : the circle is 4 units.

Solution

To calculate the area of a circle, we use the formula:

A=πr2A = \pi r^2

Where:

  • AA is the area of the circle,
  • π\pi is approximately 3.14 (as per your instruction),
  • rr is the radius of the circle.

Given that the diameter of the circle is 4 units, we first need to find the radius. The radius is half of the diameter:

r=42=2unitsr = \frac{4}{2} = 2 \, \text{units}

Now, using the formula for the area:

A=3.14×(2)2=3.14×4=12.56square unitsA = 3.14 \times (2)^2 = 3.14 \times 4 = 12.56 \, \text{square units}

Rounding to one decimal place:

A12.6square unitsA \approx 12.6 \, \text{square units}

So, the area of the circle is approximately 12.6 square units.


Would you like further details or clarifications on this? Here are a few related questions:

  1. How do you find the circumference of a circle?
  2. What if the radius was 3 units instead of 2 units, how would the area change?
  3. How is the value of π\pi used in real-world applications?
  4. How does the formula for the area of a circle differ from the area of a square?
  5. What is the formula to calculate the volume of a sphere?

Tip: Remember that the radius is always half of the diameter in a circle!

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Math Problem Analysis

Mathematical Concepts

Geometry
Circle Area Calculation

Formulas

Area of a circle: A = πr²

Theorems

Radius is half the diameter

Suitable Grade Level

Grades 6-8