To calculate the volume of a cone, we can use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where:
- \( V \) is the volume,
- \( r \) is the radius of the base,
- \( h \) is the height of the cone.
From the provided information:
- The base radius \( r = 9 \) inches,
- The perpendicular height \( h = 5 \) inches,
- We will use \( \pi \approx 3.14 \).
Now, substitute the values into the formula:
\[ V = \frac{1}{3} \times 3.14 \times (9)^2 \times 5 \]
Calculate \( (9)^2 \):
\[ (9)^2 = 81 \]
Now substitute this value in:
\[ V = \frac{1}{3} \times 3.14 \times 81 \times 5 \]
Calculate \( 81 \times 5 \):
\[ 81 \times 5 = 405 \]
Now substitute back into the formula:
\[ V = \frac{1}{3} \times 3.14 \times 405 \]
Calculate \( 3.14 \times 405 \):
\[ 3.14 \times 405 \approx 1273.7 \]
Finally, divide by 3:
\[ V = \frac{1273.7}{3} \approx 424.5667 \]
Therefore, the volume of the cone is approximately \( 423.9 \) cubic inches when rounded.
Thus, the correct answer is:
423.9 cubic inches.
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