SSC CGL 2024 Tier-I · 19 September 2024, Shift 3 · Quantitative Aptitude · Question 19 of 99

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.

The total surface area of a closed cube is given as 1152 cm 2 . What is the length (in cm) of each side of the cube?

Answer

Why

Correct — D. A closed cube has six equal square faces, so its total surface area is 6a².

6a² = 1152
a² = 1152 ⁄ 6 = 192
a = √192 = √(64 × 3) = 8√3 → option (d)

Check: 6 × (8√3)² = 6 × 192 = 1152 cm².

Why the others are wrong

(a)
4√13 is √208, and six such faces give 1248 cm², not 1152. Note that √192 = 4√12, which reduces further to 8√3 — 13 never enters the arithmetic.
(b)
8√2 squares to 128, so a cube of that edge has a surface area of 768 cm². The face area this question fixes is 192.
(c)
9√2 squares to 162, not 192, so the very first step fails; six such faces would total 972 cm².

Concept

A cube of edge a carries three standard measures, and mixing them is the usual loss of a mark:

Total surface area = 6a² (all six faces), lateral surface area = 4a² (the four sides), volume = a³.

Given any one of them you recover a by undoing that formula — here a = √(TSA ⁄ 6). The last move is surd simplification: pull out the largest perfect square factor, 192 = 64 × 3, so √192 = 8√3.

Every option is written in simplified surd form, which is itself a hint that 1152 ⁄ 6 will not be a perfect square. Leaving the answer as √192 is not wrong, but it will not appear on the screen.

Key facts

A closed cube has total surface area 6a², whereas a lidless cubical box has only five faces and 5a².
1152 ⁄ 6 = 192, and 192 = 64 × 3, so √192 = 8√3.
Lateral surface area of a cube is 4a², the four vertical faces only.
Surface area scales as a² and volume as a³, so a value fitting one will not fit the other.

Study next

Recovering a cube's edge from its volume with a = ∛VSimplifying a surd by extracting the largest perfect-square factorLateral versus total surface area for a cube and for a cuboid

Common traps

Dividing 1152 by 4 (lateral faces) instead of 6 for a closed cube.
Reading total surface area as the area of a single face.
Stopping at √192 or at 4√12 when the options are fully simplified.

SSC asks the same recovery from the other measure at 24 Sep 2024, 12:30, Quant Q.6 — the edge of a cube whose volume is 13,824 cm³, keyed 24.

Mensuration also runs through the sector at Quant Q.8 of this shift, where a given area and central angle fix the radius.

Related PYQs

No directly related past PYQ was found.