SSC CGL Quant – Mensuration 2D & 3D – Level 1 · Warm-up · Tier I Level

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SSC CGL Quant – Mensuration 2D & 3D – Level 1 · Warm-up · Tier I Level – 12 questions, subject: Quantitative Aptitude. Every question has the correct answer with a one-line explanation; tap "Show Answer". Free practice for TNPSC, UPSC, SSC, Bank and RRB exams – Shanmugam IAS Academy, Coimbatore.

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1.  
The diagonal of a square is 12√2 cm. What is its area?

Correct Answer: C [144 cm²]

Explanation:

Side = 12√2/√2 = 12 → area 144 (or d²/2 = 288/2 = 144).

2.  
A rectangular plot measures 24 m by 18 m. What is the length of its diagonal?

Correct Answer: D [30 m]

Explanation:

24-18 = 6 × (4-3) → diagonal 6 × 5 = 30 m (Triplet Radar).

3.  
Find the area of a circle of radius 14 cm. (Take π = 22/7)

Correct Answer: B [616 cm²]

Explanation:

22/7 × 14 × 14 = 616 cm² (88 is the circumference).

4.  
What is the area of an equilateral triangle of side 8 cm?

Correct Answer: A [16√3 cm²]

Explanation:

√3/4 × 64 = 16√3 cm².

5.  
The parallel sides of a trapezium are 13 cm and 19 cm, and the distance between them is 8 cm. Its area is:

Correct Answer: D [128 cm²]

Explanation:

½ × (13 + 19) × 8 = 16 × 8 = 128 cm².

6.  
The total surface area of a cube is 150 cm². What is its volume?

Correct Answer: A [125 cm³]

Explanation:

6a² = 150 → a = 5 → a³ = 125 cm³.

7.  
Find the volume of a cylinder of radius 7 cm and height 12 cm. (Take π = 22/7)

Correct Answer: B [1848 cm³]

Explanation:

πr²h = 22/7 × 49 × 12 = 1848 cm³ (528 is the curved surface area).

8.  
A cone has base radius 5 cm and height 12 cm. Its slant height is:

Correct Answer: C [13 cm]

Explanation:

l = √(5² + 12²) = √169 = 13 cm.

9.  
What is the surface area of a sphere of radius 3.5 cm? (Take π = 22/7)

Correct Answer: C [154 cm²]

Explanation:

4πr² = 4 × 22/7 × 12.25 = 154 cm².

10.  
Statement-basedWhich of the following is/are correct?
I. A cone holds one-third of a cylinder with the same base and height.
II. The total surface area of a solid hemisphere is 2πr².

Correct Answer: D [Only I]

Explanation:

I is true (⅓πr²h). II is false: TSA = 2πr² (curved) + πr² (flat) = 3πr².

11.  
Match the following
P. Lateral surface of a cuboid Q. Curved surface of a cone R. Volume of a sphere
1. πrl 2. 4/3 πr³ 3. 2h(l + b)

Correct Answer: A [P-3, Q-1, R-2]

Explanation:

Four walls = 2h(l + b); cone curved surface = πrl; sphere volume = 4/3 πr³.

12.  
Find the area of a sector of radius 14 cm and angle 45°. (Take π = 22/7)

Correct Answer: B [77 cm²]

Explanation:

45/360 × 616 = 616/8 = 77 cm² (11 cm is the arc length).

➤ Full notes, shortcuts and every answer explained – SSC CGL 2026 Quantitative Aptitude book (₹149): www.shanmugamiasacademy.in/study-materials/ssc-cgl-quantitative-aptitude

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