SSC CGL Quant – Mensuration 2D & 3D – Tier II Level · Marathon

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SSC CGL Quant – Mensuration 2D & 3D – Tier II Level · Marathon – 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.  
A regular right pyramid has an equilateral triangle of side 6 cm as base and height 8 cm. Find its volume.

Correct Answer: A [24√3 cm³]

Explanation:

Base = √3/4 × 36 = 9√3; V = ⅓ × 9√3 × 8 = 24√3 cm³.

2.  
A sector of radius 28 cm and angle 90° is folded to form a cone (no overlap). Find the base radius of the cone.

Correct Answer: C [7 cm]

Explanation:

Arc = 90/360 × 2π × 28 = 14π = 2πr → r = 7 cm (= 28 × 90/360).

3.  
Rain of 5 cm falls on a flat roof 22 m × 20 m. All the water goes into a cylindrical tank of diameter 2 m. How high does the water rise in the tank? (Take π = 22/7)

Correct Answer: D [7 m]

Explanation:

Water = 22 × 20 × 0.05 = 22 m³ = 22/7 × 1² × h → h = 7 m.

4.  
The length, breadth and height of a cuboid are increased by 10%, 20% and 25% respectively. Its volume increases by:

Correct Answer: B [65%]

Explanation:

1.1 × 1.2 × 1.25 = 1.65 → 65% increase.

5.  
A right prism has a regular hexagon of side 4 cm as its base and a height of 5 cm. Find its volume.

Correct Answer: A [120√3 cm³]

Explanation:

Base = 3√3/2 × 16 = 24√3; V = 24√3 × 5 = 120√3 cm³.

6.  
A hemispherical bowl of internal radius 9 cm is full of juice. It is poured into cylindrical bottles of radius 1.5 cm and height 4 cm. How many bottles are filled?

Correct Answer: C [54]

Explanation:

⅔π × 729 = 486π; bottle = π × 2.25 × 4 = 9π → 486 ÷ 9 = 54.

7.  
A toy is a hemisphere of radius 6 cm with a cone of the same radius and height 8 cm on it. Find the total surface area of the toy.

Correct Answer: D [132π cm²]

Explanation:

Only outer surfaces: 2πr² + πrl = 72π + 60π = 132π cm² (l = 10; the flat circle is hidden).

8.  
What is the area of a regular octagon of side 2 cm?

Correct Answer: A [8(1 + √2) cm²]

Explanation:

Octagon area = 2(1 + √2)a² = 2(1 + √2) × 4 = 8(1 + √2) cm².

9.  
A triangle has sides 7 cm, 15 cm and 20 cm. What is its circumradius?

Correct Answer: C [12.5 cm]

Explanation:

s = 21; area = √(21 × 14 × 6 × 1) = 42; R = abc ÷ (4 × area) = 2,100 ÷ 168 = 12.5 cm.

10.  
All eight edges of a square pyramid are 10 cm long. Find its volume.

Correct Answer: B [500√2/3 cm³]

Explanation:

Half-diagonal of base = 5√2; h = √(100 − 50) = 5√2; V = ⅓ × 100 × 5√2 = 500√2/3 cm³.

11.  
Two-quantity comparison
Quantity I: Curved surface area of a sphere of radius r
Quantity II: Curved surface area of the cylinder that just encloses the sphere

Correct Answer: C [Quantity I = Quantity II]

Explanation:

Cylinder: radius r, height 2r → 2πr × 2r = 4πr² = sphere's surface.

12.  
Water flows at 7 m/s through a pipe of internal radius 1 cm into a cylindrical tank of radius 40 cm. In how much time does the water level rise by 63 cm?

Correct Answer: A [2 min 24 s]

Explanation:

Flow = π × 1² × 700 = 700π cm³/s; need π × 1600 × 63 → 1600 × 63 ÷ 700 = 144 s.

➤ 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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