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
To calculate the volume of a cone, you use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius of the base of the cone and \( h \) is the height of the cone.
Given:
- The base radius of the cone \( r \) is 9 inches.
- The slant height (the diagonal line) is not directly used in the formula and there might be a confusion because we need the perpendicular height from the apex to the center of the base within the cone. We were provided the perpendicular height outside the cone, which is also the true height we need for the formula.
So, using the height \( h = 5 \) inches (the perpendicular height from the apex to the base), we can substitute the values into the formula to find the volume:
\[ V = \frac{1}{3} \pi (9)^2 (5) \]
\[ V = \frac{1}{3} \pi (81) (5) \]
\[ V = \frac{1}{3} (405\pi) \]
\[ V = 135\pi \]
Now, we need to approximate as the question does not specify using \( \pi \) as 3.14 or a simplified form. Taking \( \pi \) as 3.14:
\[ V \approx 135 \times 3.14 \]
\[ V \approx 423.9 \text{ cubic inches} \]
So, the volume of the cone is approximately \( 423.9 \text{ cubic inches} \). The response that most closely matches this value is 423 cubic inches, although it is not entirely accurate as it lacks the decimal portion. It seems like there might have been a rounding or typographical error in the provided responses, but 423 cubic inches can be considered the correct answer from the given options.