To find the volume of a cone, you can use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where:
- \( V \) is the volume,
- \( r \) is the radius of the base of the cone,
- \( h \) is the height of the cone.
From the problem, the height \( h \) of the party hat (cone) is given as 8 inches. The width is 6 inches, which refers to the diameter of the base of the cone. Therefore, the radius \( r \) can be calculated as follows:
\[ r = \frac{diameter}{2} = \frac{6}{2} = 3 \text{ inches} \]
Now substituting the values \( r = 3 \) inches and \( h = 8 \) inches into the volume formula:
\[ V = \frac{1}{3} \pi (3)^2 (8) \]
Calculating this step-by-step:
- Calculate \( r^2 \):
\[ r^2 = 3^2 = 9 \]
- Substitute \( r^2 \) in the volume formula:
\[ V = \frac{1}{3} \pi (9)(8) \]
- Calculate \( 9 \times 8 \):
\[ 9 \times 8 = 72 \]
- Now substitute this into the volume formula:
\[ V = \frac{1}{3} \pi (72) \]
- Multiply \( 72 \) by \( \frac{1}{3} \):
\[ \frac{72}{3} = 24 \]
- Finally, multiply by \( \pi \):
\[ V = 24 \pi \]
Using \( \pi \approx 3.14\):
\[ V \approx 24 \times 3.14 \approx 75.36 \text{ in}^3 \]
Thus, rounding to one decimal place, the volume of the cone is approximately \( 75.4 \text{ in}^3 \).
The measurement closest to the volume of the party hat is:
\[ \boxed{75.4 , \text{in}^3} \]