Creating a frustum, a right circular cone is sliced parallel to its base,. The height of the original cone is 30 cm, and the cut is made 10 cm from the vertex. What is the ratio of the volumes of the frustum to that of the entire cone?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 26:27.
Original cone height H = 30 cm, cut height from the vertex h = 10 cm
For similar cones, volume ratio = (height ratio)3
(Small cone volume)/(Whole cone volume) = (10/30)3 = (1/3)3 = 1/27
⇒ Small cone volume = (1/27) × Whole cone volume
Frustum volume = Whole cone volume – Small cone volume
= Whole cone volume – (1/27) × Whole cone volume
= (26/27) × Whole cone volume
⇒ Frustum volume/Whole cone volume = 26/27
Ratio of frustum volume to whole cone volume = 26:27