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
235.5 cubic inches
235.5 cubic inches
47.1 cubic inches
47.1 cubic inches
423.9 cubic inches
423.9 cubic inches
942 cubic inches
To find the volume of the cone, we can use the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone.
Given that the base radius is 9 inches, we can use this value for r. However, the given height of 5 inches is the perpendicular distance from the apex to the base outside the cone. To find the actual height of the cone, we need to subtract the radius from this perpendicular height.
Actual height of the cone = 5 inches - 9 inches = -4 inches (negative because it is below the base)
Now, let's find the volume using the formula:
V = (1/3)π(9^2)(-4) = 6π(81)(-4) = -1,936π
The volume of the cone is approximately -1,936π cubic inches.
None of the given options match this result, so none of them are correct.