Problem 11 - Elementary Algebra

Question

Find the area of a circle with a radius of \(6 \mathrm{~cm}\).

Step-by-Step Solution

Answer

The area of the circle is \(113.04 \mathrm{~cm}^2\).

Step 1 - Recall the Area Formula for a Circle

The area of a circle is given by the formula \( A = \pi r^2 \). In this formula, \(A\) represents the area, \(\pi\) is a constant approximately equal to 3.14159, and \(r\) represents the radius of the circle.

Step 2 - Substitute the Radius into the Formula

Given that the radius \(r\) is \(6 \mathrm{~cm}\), substitute this value into the formula: \[ A = \pi (6)^2 \] \[ A = \pi \, \times \, 36 \] \[ A = 36 \pi \]

Step 3 - Calculate the Numerical Value

To find the numerical value, approximate \(\pi\) as 3.14 (or use the \(\pi\) button on a calculator): \[ A \approx 36 \, \times \, 3.14 \] \[ A \approx 113.04 \mathrm{~cm}^2 \]

Key Concepts

circle area formula

The area of a circle specifies the amount of space inside the circle's boundary. To calculate this, we use a special formula. The circle area formula is:
\[ A = \pi r^2 \]
Here,

• \(A\) stands for the area.
• \( \pi \), pronouced 'pi', is a constant.
• \( r \) is the radius, which is the distance from the center of the circle to any point on its edge.

The formula tells us that to find the area, we square the radius (\