Maths question from Panchayat Secretary (VLW) exam, 2025 by JKSSB
Two right circular cones and a right circular cylinder are taken, all of which have the same radius and the same height. The bases of cones are joined to two bases of cylinder. What would be the ratio of total volume of structure formed to volume of right circular cylinder?
Last updated Jun 13, 2026
Correct Answer:
Option D —
5/3
To find the correct ratio, we can look at how the volume of a cone compares to the volume of a cylinder when they share the exact same radius and height.
There is a well-known rule in geometry regarding these shapes: the space inside a single cone is exactly one-third of the space inside a cylinder with the same dimensions.
Breaking Down the Structure
The new structure is made by taking one central cylinder and attaching a cone to each of its two flat ends. Therefore, the total volume of the new structure is the sum of:
The volume of the cylinder
The volume of the first cone
The volume of the second cone
Since each cone is worth one-third of a cylinder, we can think of the total volume in terms of "cylinder units":
The central cylinder equals one cylinder unit.
The first cone equals one-third of a cylinder unit.
The second cone equals one-third of a cylinder unit.
Adding these all together, one plus one-third plus one-third gives us five-thirds of a cylinder unit.
Finding the Ratio
The question asks for the ratio of the total volume of this new structure to the volume of the original cylinder alone.
Since the structure is equal to five-thirds of a cylinder, and we are comparing it to exactly one cylinder, the ratio is simply five to three, which can be written as five over three.
Conclusion
The correct option is (D) 5/3.
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
