To find the length of string needed to go around the bottom of a cone-shaped hat, we need to calculate the circumference of the base of the cone. The formula for the circumference \( C \) of a circle is given by:
\[ C = 2\pi r \]
where \( \pi \) is approximately 3.14 and \( r \) is the radius.
Given that the radius \( r \) is 4 inches, we can substitute the values into the formula:
\[ C = 2 \times 3.14 \times 4 \]
Calculating this:
\[ C = 2 \times 3.14 \times 4 = 6.28 \times 4 = 25.12 \text{ inches} \]
Therefore, the amount of string needed to go around the bottom of the hat is 25.12 inches.
The correct response is B: 25.12 inches.
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