SSC CGL 2025 Tier-I · 15 September 2025, Shift 1 · Quantitative Aptitude · Question 17 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 13 September 2026.

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A pyramid has a base area of 60 cm² and height 9 cm. What is its volume?

(a)180 cm³
(b)280 cm³
(c)240 cm³
(d)160 cm³

Answer

Why

Correct — A. A pyramid holds one-third of the prism on the same base and height.

Volume = (1⁄3) × base area × height
= (1⁄3) × 60 × 9
= 60 × 3 = 180 cm³ → option (a)

Why the others are wrong

(b)
280 cm³ — 280 cm³ would need a height of 280 × 3 ÷ 60 = 14 cm. With the stated 9 cm, one-third of 60 × 9 is 180.
(c)
240 cm³ — 240 cm³ would need a height of 240 × 3 ÷ 60 = 12 cm, not the 9 cm the question gives.
(d)
160 cm³ — 160 cm³ would need a height of 160 × 3 ÷ 60 = 8 cm. The height is 9 cm, so the volume is (1⁄3) × 60 × 9 = 180.

Concept

Volume of any pyramid = (1⁄3) × base area × height, whatever the shape of the base: square, triangle or any other polygon. Here the base area is given directly, so no base formula is needed.

The one-third compares the pyramid with a prism on the same base and height, whose volume is base × height = 540 cm³. The pyramid holds a third of it.

Key facts

Pyramid volume = (1⁄3) × base area × height.
A prism on the same base and height holds three times as much: 60 × 9 = 540 cm³.
A cone is the circular-base case: (1⁄3)πr²h.

Study next

Pyramids on equilateral-triangle bases, where base area = (√3⁄4)a²Square-base pyramids given the diagonal, where base area = d²⁄2Composite solids, such as a pyramid set on a cube

Common traps

Leaving out the 1⁄3, which gives 540 cm³, the prism's volume.

21 Sep 2025, 16:00, Quant Q.6 sets a pyramid with a triangular base of side 10 cm and height 14 cm on a cube: 1000 + 202.07 = 1202.07 cm³.

Tier-II applies the same one-third rule at 19 Jan 2026, 11:00 AM, Maths Q.20 (triangular base) and 19 Jan 2026, 11:00 AM, Maths Q.24 (square base given by its diagonal).

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 99 SSC CGL questions on it, every solved shift.