SSC CGL Quant – Mensuration 2D & 3D – Level 3 · Challenge
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I (2³ = 8) and II (2² = 4) are true; III is false – the volume becomes 4 times.
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SSC CGL Quant – Mensuration 2D & 3D – Level 3 · Challenge – 8 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 solid sphere of radius 3 cm is dropped into a cylindrical vessel of radius 6 cm partly filled with water. By how much does the water level rise?
Correct Answer: C [1 cm]
Explanation:
πR²h = 4/3 πr³ → 36h = 36 → h = 1 cm.
2.
Each side of a rhombus is 17 cm and one diagonal is 16 cm. Find its area.
Correct Answer: B [240 cm²]
Explanation:
Half-diagonals 8 and √(289 − 64) = 15 → diagonals 16 and 30 → ½ × 16 × 30 = 240 cm².
3.
Find the area of the circle inscribed in an equilateral triangle of side 6√3 cm.
Correct Answer: B [9π cm²]
Explanation:
Inradius = a/(2√3) = 6√3/(2√3) = 3 → area 9π (36π is the circumcircle).
4.
Assertion–Reason
A: A cylinder holds three times as much as a cone with the same base radius and height.
R: The volume of a cone is ⅓πr²h.
A: A cylinder holds three times as much as a cone with the same base radius and height.
R: The volume of a cone is ⅓πr²h.
Correct Answer: C [Both A and R are true and R explains A]
Explanation:
Cylinder πr²h ÷ cone ⅓πr²h = 3, so R explains A.
5.
A conical tent has radius 14 m and height 48 m. How many metres of canvas 1.1 m wide are needed to make it? (Take π = 22/7)
Correct Answer: D [2000 m]
Explanation:
l = 50; curved area = 22/7 × 14 × 50 = 2,200 m² → 2,200 ÷ 1.1 = 2,000 m.
6.
The largest possible sphere is carved out of a wooden cube of edge 14 cm. What volume of wood is wasted? (Take π = 22/7)
Correct Answer: A [1306⅔ cm³]
Explanation:
Sphere r = 7: 4/3 × 22/7 × 343 = 1437⅓; 2744 − 1437⅓ = 1306⅔ cm³.
7.
A solid metal cylinder of radius 3 cm and height 5 cm is melted and recast into cones of radius 1 cm and height 3 cm. How many cones are made?
Correct Answer: B [45]
Explanation:
π × 9 × 5 = 45π; each cone = ⅓π × 1 × 3 = π → 45 cones.
8.
True/False countHow many of these statements are true?
I. Doubling the radius of a sphere makes its volume 8 times.
II. Doubling every edge of a cube makes its surface area 4 times.
III. Doubling the radius of a cylinder (same height) doubles its volume.
I. Doubling the radius of a sphere makes its volume 8 times.
II. Doubling every edge of a cube makes its surface area 4 times.
III. Doubling the radius of a cylinder (same height) doubles its volume.
Correct Answer: D [Only 2]
Explanation:
I (2³ = 8) and II (2² = 4) are true; III is false – the volume becomes 4 times.
➤ 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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