Maths question from Panchayat Secretary (VLW) exam, 2025 by JKSSB
A cuboid is taken and divided into two equal parts such that each part is a cube. Which of these will be definitely TRUE?
Last updated May 30, 2026
Correct Answer:
Option C —
No two edges of cuboid are of equal length
To determine which statement is definitely true, we can visualize the shape of the cuboid based on how it is divided.
Step 1: Understand the structure of the divided cuboid
The problem states that when the cuboid is cut into two equal parts, each part becomes a perfect cube. A cube is a three-dimensional shape where all sides (length, width, and height) are exactly equal to each other.
Step 2: Reconstruct the original cuboid
If you glue those two identical cubes back together to form the original cuboid, you are placing them side-by-side along one face.
The width of the cuboid remains the same as the cube's width.
The height of the cuboid remains the same as the cube's height.
The length of the cuboid becomes exactly twice the length of one cube (since two cubes are joined together).
Step 3: Analyze the relationship between the sides
Because two of the dimensions (width and height) are equal to the cube's side length, and the third dimension (length) is exactly twice that side length, the original cuboid has a specific proportion. If you compare the short side to the long side, the relationship is exactly 1 to 2.
Let's evaluate the options based on this:
(A) is false because a cuboid with one side twice as long as the others is not a cube.
(C) is false because two of the sides (width and height) are of equal length.
(D) is false because the problem itself tells us it was divided into two identical cubes.
Therefore, the ratio of a pair of sides of the cuboid must be 1 to 2.
Correct Answer: (B) The ratio of a pair of sides of cuboid is 1:2
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
