SSC CGL 2025 Tier-I · 15 September 2025, Shift 1 · Quantitative Aptitude · Question 15 of 100

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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SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

How many hemispheres with a radius of 3 cm can be produced by melting down a hemisphere with a radius of 12 cm?

(a)32
(b)64
(c)12
(d)54

Answer

Why

Correct — B. Melting keeps the volume, so divide the large volume by one small volume.

Large: (2⁄3)π × 12³ = (2⁄3)π × 1728 = 1152π
Small: (2⁄3)π × 3³ = (2⁄3)π × 27 = 18π

Number = 1152π ÷ 18π = 64 → option (b)

Shortcut: (12 ÷ 3)³ = 4³ = 64.

Why the others are wrong

(a)
32 — 32 is the number of full spheres of radius 3 cm, each (4⁄3)π × 27 = 36π: 1152π ÷ 36π = 32. The pieces here are hemispheres, half that size, so there are twice as many.
(c)
12 — 12 hemispheres of 18π use only 216π of the 1152π. The radius shrinks by a factor of 4, and the volume by 4³ = 64, not by 12.
(d)
54 — 54 hemispheres use 54 × 18π = 972π, leaving 180π of metal, enough for 10 more. The full count is 1152π ÷ 18π = 64.

Concept

Volume scales with the cube of the radius. A hemisphere of radius 12 is a hemisphere of radius 3 enlarged 4 times in every direction, so it holds 4³ = 64 times the metal.

The shortcut needs the same shape on both sides: hemisphere to hemisphere, or sphere to sphere. Mixing shapes needs the full volume formulas.

Key facts

Volume of a hemisphere = (2⁄3)πr³.
Solids of the same shape: volume ratio = (ratio of radii)³.
A sphere of radius r holds the metal of two hemispheres of radius r.

Study next

Recasting a sphere into cones or cylinders of a given sizeTwo solids melted into one: R³ = r₁³ + r₂³ for the same shapeSurface-area comparisons after recasting

Common traps

Using the radius ratio 4, or its square 16, instead of the cube 64.
Using the full-sphere volume for the small pieces, which halves the count to 32.

18 Sep 2025, 12:30, Quant Q.11 runs the volume balance the other way, adding the cubes of 2 and 4 to recast two hemispheres into one. 15 Sep 2025, 09:00, Quant Q.14 melts a sphere into 8 equal spheres, so each has half the radius.

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.