SSC CGL 2025 Tier-II · Paper-I, 19 January 2026 · Mathematical Abilities · Question 20 of 150

We transcribed this text from the pictures of a candidate's response sheet for this paper; the answer is the key SSC marked with a green tick on that sheet. Solution last reviewed 11 September 2026.

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The base of a right pyramid is an equilateral triangle with side 10 cm, and its vertical height is 24 cm. Find the volume (in cm³) of the pyramid.

(a)100√3cm³
(b)400√3 cm³
(c)150√3 cm³
(d)200√3 cm³

Answer

Why

Correct — D. A pyramid's volume is one-third of base area × height.

Base area of the equilateral triangle: (√3⁄4) × 10² = 25√3 cm²
Multiply by the vertical height: 25√3 × 24 = 600√3
Take one-third: 600√3 ÷ 3 = 200√3 cm³ → option (d)

Why the others are wrong

(a)
100√3cm³ — 100√3 would need a height of 12 cm on this base: (1⁄3) × 25√3 × 12 = 100√3. The stem gives the vertical height as 24 cm, which doubles it.
(b)
400√3 cm³ — 400√3 uses a base of 50√3, which is side × the triangle's height, 10 × 5√3, without the ½. A triangle's area is ½ × 10 × 5√3 = 25√3.
(c)
150√3 cm³ — 150√3 is 600√3 ÷ 4, dividing base area × height by 4 instead of 3. The pyramid formula divides by 3: 600√3 ÷ 3 = 200√3.

Concept

Every pyramid, like every cone, has V = (1⁄3) × base area × height, where the height is the perpendicular height from the apex to the base, not the slant height.

The base shape changes only the area step. An equilateral triangle of side a has height (√3⁄2)a, so its area is ½ × a × (√3⁄2)a = (√3⁄4)a².

A prism on the same base and height would hold 25√3 × 24 = 600√3 cm³, three times the pyramid.

Key facts

Volume of a pyramid = (1⁄3) × base area × vertical height.
Area of an equilateral triangle of side a = (√3⁄4)a².
Height of an equilateral triangle of side a = (√3⁄2)a.
A pyramid holds one-third of the prism with the same base and height.

Study next

Pyramids on a square base when only the diagonal is givenSlant height and lateral surface area of a regular pyramidVolume of a triangular prism: base area × length

Common traps

Using a slant height in place of the vertical height: the formula needs the perpendicular height.
Dropping the (1⁄3), which gives the prism's 600√3 cm³.

Here the base is equilateral, so the area step needs (√3⁄4)a².

The same base, side 10 cm, sits under a 14 cm pyramid at 21 Sep 2025, 16:00, Quant Q.6, and 19 Jan 2026, 11:00 AM, Maths Q.24 applies the one-third rule to a square base known only 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 56 SSC CGL questions on it, every solved shift.