A right circular cone is divided into two sections by a plane that is parallel to the base, with the volumes of the frustum and the smaller cone having a ratio of 7 : 1. Determine the ratio of their heights.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 1 : 1.
Let height of original cone = H, height of smaller cone = h
(Smaller cone volume)/(Original cone volume) = (h/H)3
Frustum volume : smaller cone volume = 7 : 1
Original cone volume = 7 + 1 = 8 parts, and smaller cone = 1 part
(h/H)3 = 1/8
⇒ h/H = 1/2
⇒ h = H/2
Frustum height = H – H/2 = H/2
Ratio of heights (frustum : smaller cone) = (H/2) : (H/2) = 1 : 1