Use the image to answer the question.
An oblique cone shows a base radius of 9 inches. The perpendicular height is 5 inches from the apex to the base outside the cone. A right angle is formed outside the cone to the right. A dashed diagonal line connects the center of the circular base to the apex.
What is the volume of the cone?
(1 point)
Responses
47.1 cubic inches
47.1 cubic inches
235.5 cubic inches
235.5 cubic inches
942 cubic inches
942 cubic inches
423.9 cubic inches
To calculate the volume of a cone, use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( V \) is the volume, \( r \) is the base radius, and \( h \) is the height of the cone.
In this case, the radius \( r = 9 \) inches, and the slant height (the dashed line) is not needed for the volume calculation since you have the perpendicular height from the apex to the base outside the cone, which is the true height of the cone involved in the volume calculation, \( h = 5 \) inches.
Plugging the values into the formula:
\[ V = \frac{1}{3} \pi (9)^2 (5) \]
\[ V = \frac{1}{3} \pi (81)(5) \]
\[ V = \frac{1}{3} \pi (405) \]
\[ V = 135 \pi \]
Now, we can calculate the numerical value using the approximate value for \( \pi \), which is \( 3.14159 \):
\[ V \approx 135 \times 3.14159 \]
\[ V \approx 424.47 \text{ cubic inches} \]
The closest answer among your given options is:
423.9 cubic inches.