SSC CGL 2024 Tier-I · 24 September 2024, Shift 2 · Quantitative Aptitude · Question 6 of 100

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 10 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.

What is the length (in cm) of each side of a cube if the volume of a cube is 13,824 cm 3 ?

(a)20.4
(b)24
(c)34
(d)22

Answer

Why

Correct — B. The volume of a cube is a³, so the edge is the cube root of 13,824.

Factorise by halving: 13,824 = 2⁹ × 27
27 = 3³, so 13,824 = 2⁹ × 3³ = (2³ × 3)³
Cube root = 2³ × 3 = 24

Check by multiplying back: 24² = 576 and 576 × 24 = 13,824 → option (b).

Why the others are wrong

(a)
20.4 — 20.4³ is about 8,490, well short of 13,824. And 13,824 is a perfect cube, so the edge is a whole number and a decimal can be dropped on sight.
(c)
34 — 34³ = 39,304, nearly three times the given volume. 34 carries a factor of 17, and 13,824 has none.
(d)
22 — 22³ = 10,648, still short. 22 carries a factor of 11, which does not appear in 13,824 = 2⁹ × 3³.

Concept

The volume of a cube is a³, so recovering the edge means taking a cube root. The reliable route is prime factorisation — split the number into primes, then take one prime out of every group of three.

13,824 = 2⁹ × 3³. Nine 2s make three complete groups and give 2³ = 8; the three 3s give one 3. The edge is 8 × 3 = 24.

Worth carrying into the hall: 12³ = 1,728, 18³ = 5,832 and 24³ = 13,824.

The stem prints the units as "cm 3", which is cm³ with the superscript flattened by the response sheet. Read it as a volume.

Key facts

Volume of a cube = a³, so the edge is the cube root of the volume.
Total surface area of a cube = 6a², another route SSC uses to hand you the edge.
Cube-rooting by factorisation means taking one factor from each triple of identical primes.
13,824 = 2⁹ × 3³ = 24³.

Study next

Recovering the edge from total surface area using 6a²Cube roots by factorisation for numbers such as 4,096 and 9,261Volume and surface area of a cuboid, where the three edges differ

Common traps

Dividing 13,824 by 3 instead of taking a cube root
Taking a square root and landing near 117.6
Eliminating by rough estimate without noticing that 13,824 is an exact cube

SSC hands you one measurement of a cube and asks for another. Here it is volume to edge. At 19 Sep 2024, 16:00, Quant Q.19 the given quantity is the total surface area of a closed cube, which needs 6a² rather than a³.

The cube root can also be step one rather than the answer. At 18 Sep 2024, 09:00, Quant Q.5 three cubes of volume 512 cm³ are joined end to end, so the edge 8 cm must be recovered before the cuboid's surface area can be found.

Related PYQs

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