SSC CGL 2025 Tier-I · 19 September 2025, Shift 1 · Quantitative Aptitude · Question 10 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 11 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.

A hemisphere of radius 5 cm is carved from a sphere. What is the volume of the hemisphere?

(a)65π⁄6 cm³
(b)125π⁄6 cm³
(c)250π⁄3 cm³
(d)375π⁄6 cm³

Answer

Why

Correct — C.
Hemisphere volume = (2⁄3)πr³, half of the sphere's (4⁄3)πr³.
Cube the radius: r³ = 5³ = 125
Multiply: (2⁄3) × 125 × π = 250π⁄3 cm³ → option (c).

Why the others are wrong

(a)
65π⁄6 cm³ — 65π⁄6 ≈ 10.8π is far below the true 250π⁄3 ≈ 83.3π. Its numerator, 65, has no factor 5³ = 125, which (2⁄3)πr³ with r = 5 must carry.
(b)
125π⁄6 cm³ — 125π⁄6 is πr³⁄6, one-quarter of the answer. It is what the sphere formula πd³⁄6 gives when 5 cm is read as the diameter of a whole sphere.
(d)
375π⁄6 cm³ — 375π⁄6 simplifies to 125π⁄2, which is (1⁄2)πr³. The hemisphere coefficient is 2⁄3, not 1⁄2, so this is three-quarters of the true volume.

Concept

A hemisphere is exactly half a sphere, so its volume is half of (4⁄3)πr³, which is (2⁄3)πr³.

The volume depends on the radius alone, and r enters cubed: doubling r multiplies the volume by 8.

The stem says the hemisphere is carved from a sphere but never gives that sphere's size. It is not needed: the hemisphere's volume depends only on its own 5 cm radius.

Key facts

Volume of a sphere = (4⁄3)πr³.
Volume of a hemisphere = (2⁄3)πr³.
Total surface area of a solid hemisphere = 3πr², the curved 2πr² plus the flat base πr².
With r = 5 cm, r³ = 125, so the hemisphere holds 250π⁄3 ≈ 261.8 cm³.

Study next

Curved and total surface area of a hemisphereMelting and recasting solids by equating volumesHollow hemispherical shells: (2⁄3)π(R³ − r³)

Common traps

Using the sphere coefficient 4⁄3 and forgetting to halve it
Squaring the radius instead of cubing it, a surface-area habit carried into a volume question

18 Sep 2025, 12:30, Quant Q.11 uses the same (2⁄3)πr³: two hemispheres of radii 2 cm and 4 cm are recast into one, so R³ = 2³ + 4³ = 72, and its total surface area 3πR² is keyed 163 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 51 SSC CGL questions on it, every solved shift.