SSC CGL 2024 Tier-I · 23 September 2024, Shift 1 · Quantitative Aptitude · Question 17 of 97

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 6 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

Find the length of the longest stick that can be fitted in a cubical vessel of edge 70 cm.

Answer

Why

Correct — A. The longest straight object that fits inside a cube lies along its space diagonal, corner to opposite corner.

Face diagonal (Pythagoras on one face) = a√2
The space diagonal is the hypotenuse of a right triangle with legs a and a√2:
d² = a² + 2a² = 3a²
d = a√3

With a = 70: d = 70√3 cm → option (a), which is about 121.2 cm.

Why the others are wrong

(b)
35√3 cm is the space diagonal of a cube of edge 35 cm, half the one given. It is also only about 60.6 cm — shorter than the 70 cm edge, so it cannot be the longest fit.
(c)
10√3 cm is about 17.3 cm, far shorter than a single 70 cm edge, which by itself already accommodates a longer stick.
(d)
70√2 cm is the face diagonal, the longest line inside one face (about 99 cm). The space diagonal beats it because it also uses the third dimension.

Concept

A cube offers three lengths, each longer than the last: edge a, face diagonal a√2, and space diagonal a√3.

A stick 'fitted in' a vessel means the greatest distance between two points of the solid, which is the space diagonal. Build it in two Pythagoras steps — a√2 across a face, then that combined with the perpendicular edge a.

For a cuboid the same construction gives √(l² + b² + h²), of which a√3 is the case l = b = h.

The options are all surds, so no approximation of √3 is needed to choose.

'Vessel' is decoration: no wall thickness is given and none is intended, so the 70 cm edge goes straight into the formula.

Key facts

Cube of edge a: face diagonal a√2, space diagonal a√3.
Cuboid of dimensions l, b and h: longest rod = √(l² + b² + h²).
70√3 ≈ 121.24 cm, taking √3 ≈ 1.732.
A sphere inscribed in a cube has diameter a, while a cube inscribed in a sphere needs diameter a√3.

Study next

Longest rod in a cuboid, √(l² + b² + h²)Deriving the cube diagonal in two Pythagoras stepsSphere inscribed in a cube and cube inscribed in a sphere

Common traps

Answering with the face diagonal a√2, which is only the longest line within one face.
Halving the edge before applying √3.
Reaching for surface area or volume because the solid is described as a vessel.

SSC asks the same construction for a cuboid, where the arithmetic is heavier and the answer is a decimal.

The longest diagonal of a box measuring 1.2 cm × 1.3 cm × 1.5 cm, correct to two decimals, is asked at Quant Q.6 of 17 Sep 2024, 16:00. The cube version, as here, keeps the answer in surd form.

Related PYQs

No directly related past PYQ was found.