SSC CGL 2025 Tier-I · 21 September 2025, Shift 3 · Quantitative Aptitude · Question 6 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 11 September 2026.

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A pyramid with an equilateral triangular base of side 10 cm and height 14 cm is placed on top of a cube with side length 10 cm. Find the total volume of the composite solid.

(a)2102.57 cm³
(b)1202.07 cm³
(c)4202.07 cm³
(d)6202.57 cm³

Answer

Why

Correct — B.
Add the two volumes; the joined face does not change either one.

Cube: 10³ = 1,000 cm³
Base triangle: (√3⁄4) × 10² = 25√3 ≈ 43.30 cm²
Pyramid: (1⁄3) × 43.30 × 14 ≈ 202.07 cm³

Total: 1,000 + 202.07 = 1,202.07 cm³ → option (b)

Why the others are wrong

(a)
2102.57 cm³ — 2,102.57 cm³ is too big. Even a prism on the same triangle and height holds only 43.30 × 14 ≈ 606.22 cm³, so the total cannot pass 1,606.22 cm³.
(c)
4202.07 cm³ — 4,202.07 cm³ would need a 3,202.07 cm³ pyramid, over five times the 606.22 cm³ prism on the same base and height. A pyramid holds a third of that prism.
(d)
6202.57 cm³ — 6,202.57 cm³ is over six times the cube's 1,000 cm³. The pyramid on top adds only about 202 cm³, so the total is near 1,202 cm³.

Concept

A composite solid made by stacking two solids has the sum of their volumes. The joined face is only a boundary, so nothing is subtracted.

A pyramid holds one-third of the prism on the same base and height: V = (1⁄3) × base area × height.

The base here is an equilateral triangle, whose area is (√3⁄4) × side².

The base triangle's altitude is (√3⁄2) × 10 ≈ 8.66 cm, so it fits inside the cube's 10 cm square face. Where it sits on that face does not change the total volume.

Key facts

Volume of any pyramid = (1⁄3) × base area × height
Area of an equilateral triangle of side a = (√3⁄4)a², which is 25√3 ≈ 43.30 cm² for a = 10
Volume of a cube of side a = a³
Volumes of stacked solids simply add, with nothing subtracted for the joined face

Study next

Total surface area of a composite solid, where the joined faces drop outVolume of a cone standing on a cylinderSlant height and lateral surface area of a regular pyramid

Common traps

Forgetting the 1⁄3 and using base area × height, which makes the top 606.22 cm³
Using ½ × side² instead of (√3⁄4) × side² for the equilateral base

21 Sep 2025, 16:00, Quant Q.14 uses the full prism formula, volume = base area × height: 1,024 ÷ 16 = 64 cm², so the square base has the keyed side 8 cm. A pyramid on that base and height would hold a third of it.

Related PYQs

No directly related past PYQ was found.

Topic: Right Prism, Right Circular Cone, Right Circular Cylinder, Sphere, Hemispheres, Rectangular Parallelepiped, Regular Right Pyramid with triangular or square base — all 51 SSC CGL questions on it, every solved shift.