Final answer:
The height of cone c is twice the height of the smaller cone above the plane because the smaller cone's volume is 1/8 that of the original, and linear dimensions scale with the cube root of the volume.
Step-by-step explanation:
The student is seeking to find the height of cone c when a plane is parallel to the base of the cone, and creates a smaller cone with a volume that is 1/8 the volume of the original cone. To solve this, we can use the principle that the volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height.
Since the problem states that the smaller cone's volume is 1/8 of the larger cone's volume, we can infer a relationship between their dimensions. The volume of a cone is proportional to the cube of its linear dimensions, so if the volume of the smaller cone is 1/8 that of the larger one, its linear dimensions (height, radius) are ⅓ that of the larger cone. Therefore, the height of the original cone (c) is twice the height of the smaller cone above the plane, which makes answer choice (a) correct.