To solve the expression [tex]\(\frac{1}{2} \pi b^2\)[/tex], follow these clear steps:
1. Identify the formula: We are asked to find the value of [tex]\(\frac{1}{2} \pi b^2\)[/tex].
2. Assign a value to [tex]\(b\)[/tex]: Here, let's assume [tex]\(b\)[/tex] has been assigned a value. For our example, let [tex]\(b = 2\)[/tex].
3. Square the value of [tex]\(b\)[/tex]: Calculate [tex]\(b^2\)[/tex].
[tex]\[
b^2 = 2^2 = 4
\][/tex]
4. Multiply by [tex]\(\pi\)[/tex]: Next, multiply the squared value by [tex]\(\pi\)[/tex].
[tex]\[
\pi \times 4 = 4\pi
\][/tex]
5. Multiply by [tex]\(\frac{1}{2}\)[/tex]: Finally, multiply the result by [tex]\(\frac{1}{2}\)[/tex].
[tex]\[
\frac{1}{2} \times 4\pi = 2\pi
\][/tex]
6. Determine the numerical value: Using the approximation [tex]\(\pi \approx 3.141592653589793\)[/tex],
[tex]\[
2\pi \approx 2 \times 3.141592653589793 = 6.283185307179586
\][/tex]
Therefore, the calculated value of the expression [tex]\(\frac{1}{2} \pi b^2\)[/tex] when [tex]\(b = 2\)[/tex] is approximately [tex]\(6.283185307179586\)[/tex].
