SSC CGL 2025 Tier-I · 23 September 2025, Shift 1 · Quantitative Aptitude · Question 4 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.

A sphere is inscribed inside a cube. The volume of the cube is 1728 cm³. What is the total surface area of the sphere?

(a)144π cm²
(b)254π cm²
(c)196π cm²
(d)298π cm²

Answer

Why

Correct — A. An inscribed sphere touches all six faces, so its diameter equals the cube's side.

Side = ∛1728 = 12 cm
Radius = 12 ÷ 2 = 6 cm
Surface area = 4πr² = 4π × 36 = 144π cm² → option (a)

Why the others are wrong

(b)
254π cm² — 254π would need r² = 254 ÷ 4 = 63.5, a radius near 7.97 cm. The cube is 12 cm across, so the sphere's radius cannot exceed 6 cm.
(c)
196π cm² — 196π is 4π × 7², the surface of a sphere of radius 7 cm. That sphere fits a cube of side 14 cm (volume 2,744 cm³), not 1,728 cm³.
(d)
298π cm² — 298π would need r² = 74.5, a radius near 8.6 cm and a diameter over 17 cm. No such sphere fits inside a 12 cm cube.

Concept

A sphere inscribed in a cube touches the centre of each face, so its diameter equals the side a.

A sphere circumscribed about a cube passes through the eight corners instead, so its diameter equals the space diagonal, a√3.

Here the sphere is inside, so r = a⁄2 and its surface is 4π(a⁄2)² = πa². With a = 12 that is 144π straight away.

Key facts

Sphere inscribed in a cube of side a: r = a⁄2.
Sphere circumscribed about a cube of side a: r = a√3⁄2.
Surface area of a sphere = 4πr², and its volume = (4⁄3)πr³.
∛1728 = 12, since 12³ = 1,728.

Study next

Cube inscribed in a sphere, where the space diagonal equals the diameterCylinder or cone inscribed in a cubeEmpty volume between a cube and its inscribed sphere

Common traps

Taking the side, 12, as the radius: 4π × 144 = 576π, which is not an option.
Working out the volume, (4⁄3)π × 6³ = 288π, when the question asks for surface area.

The same diameter = side rule drives 19 Sep 2025, 09:00, Quant Q.11, where the sphere touches all six faces and the question asks what percentage of the cube's volume is left empty.

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.