SSC CGL 2025 Tier-I · 21 September 2025, Shift 1 · Quantitative Aptitude · Question 15 of 99

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 right prism has a base in the shape of a trapezium with parallel sides 10 cm and 6 cm, and height 4 cm. If the prism height is 15 cm, what is the volume?

(a)480 cm³
(b)240 cm³
(c)520 cm³
(d)680 cm³

Answer

Why

Correct — A. Volume of a right prism = base area × height of the prism.

Trapezium base: area = ½ × (sum of parallel sides) × its height
= ½ × (10 + 6) × 4 = ½ × 16 × 4 = 32 cm²

Volume = 32 × 15 = 480 cm³ → option (a)

Why the others are wrong

(b)
240 cm³ — 240 cm³ is exactly half of 480, the ½ of the trapezium formula applied a second time. A prism's volume is base area × height with no further ½.
(c)
520 cm³ — 520 cm³ would need a base area of 520 ÷ 15 ≈ 34.7 cm², but ½ × (10 + 6) × 4 is exactly 32 cm².
(d)
680 cm³ — 680 cm³ would need a base area of 680 ÷ 15 ≈ 45.3 cm². The trapezium's area is 32 cm², so the volume is 32 × 15 = 480.

Concept

A right prism has the same cross-section all along its length, so its volume is base area × height whatever shape the base is.

Two heights appear here. The 4 cm is the trapezium's height, the gap between its parallel sides, and belongs inside the base area. The 15 cm is the prism's height and multiplies the base area.

Trapezium area = ½ × (a + b) × h: the average of the parallel sides times the gap between them.

Key facts

Volume of a right prism = base area × height
Area of a trapezium = ½ × (sum of parallel sides) × distance between them
Lateral surface area of a right prism = base perimeter × height

Study next

Total surface area of a prism: 2 × base area + base perimeter × heightHeight of an isosceles trapezium from its slant sides by PythagorasPyramid on the same base: volume = ⅓ × base area × height

Common traps

Mixing up the two heights: the 4 cm goes into the base area, the 15 cm multiplies it
Halving again after finding the base area, which gives 240 cm³

The trapezium area alone decides 21 Sep 2025, 09:00, Quant Q.9: parallel sides 30 m and 50 m, height 20 m, ½ × 80 × 20 = 800 square meters.

A right prism on a trapezium base returns at 19 Jan 2026, 11:00, Tier-II Paper-I Quant Q.25, where the base area ½ × (10 + 20) × 12 = 180 cm² leads to a total surface area of 1368 cm².

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.