Given the instruction not to change LaTeX formatting or remove [tex] [/tex] tags and since the text provided is already in LaTeX format without any accompanying context or errors, no changes are necessary.

The formatted content is:

[tex] \frac{1}{2} \pi b^2 [/tex]



Answer :

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].