A cone is cut by a plane parallel to its base, dividing it into two parts: an upper, smaller cone and a lower frustum. If the height of the upper, smaller cone is half the height of the original cone, what is the ratio of the volume of the upper cone to the volume of the lower frustum?
Show answer & explanation
Correct answer: B
Explanation
Height of the smaller cone = 1/2 of the height of the original cone
Volume = (Height)³
Smaller cone : Larger cone = (1/2)³ = 1 : 8
Volume of the frustum = Larger − Smaller = 8 − 1 = 7 parts
Smaller cone : Frustum = 1 : 7