A right circular cone having height of 30 cm is cut by two parallel at heights 10 cm and 20 cm from the base. What is the ratio of the volumes of the three parts (from top to bottom)?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 1 : 7 : 19.
Volume of a cone = (1/3)πr2h
Heights from vertex: top part height = 10, Middle = 10, Bottom = 10
Volumes of cones are proportional to the cube of height from the vertex.
Volumes are proportional to cube of heights from vertex = 103 : (203 – 103) : (303 – 203)
= 1000 : (8000 – 1000) : (27000 – 8000)
= 1000 : 7000 : 19000
= 1 : 7 : 19