SSC CGL 2025 Tier-II · Paper-I, 19 January 2026 · Mathematical Abilities · Question 13 of 150

We transcribed this text from the pictures of a candidate's response sheet for this paper; the answer is the key SSC marked with a green tick 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. This paper reaches us as a candidate's response sheet saved as pictures, so we transcribed the text from those pictures, and a second reader checked every question against them; where the layout carries meaning, we show the picture too. Each answer is the key SSC marked with a green tick 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. UnlockIAS wrote the solutions.

A sphere of radius 21 cm is cut into 8 identical pieces by making three mutually perpendicular cuts through its center (one along each axis). Find the total surface area of each piece in cm².

(a)625.25π cm²
(b)560πcm²
(c)450.75π cm²
(d)551.25π cm²

Answer

Why

Correct — D. Each piece is one-eighth of the ball: a curved patch plus three flat quarter-circles, one from each cut.

Square the radius: r² = 21² = 441
Curved part, one-eighth of 4πr²: 4 × 441π ÷ 8 = 220.5π
Flat faces, three quarter-circles of πr² ÷ 4 each: 3 × 441π ÷ 4 = 330.75π

Add them: 220.5π + 330.75π = 551.25π cm² → option (d)

Why the others are wrong

(a)
625.25π cm² — 625.25π is 74π more than the piece actually has. Its curved patch is 220.5π and its three flat quarter-circles are 330.75π, which total 551.25π.
(b)
560πcm² — 560π overshoots by 8.75π. Every face of the piece is worth a whole number of quarter-circles of πr² ÷ 4 = 110.25π (the curved patch is worth two), and 560 ÷ 110.25 is not a whole number.
(c)
450.75π cm² — 450.75π is about 100π short. The curved patch plus three flat quarter-circles gives 551.25π; leave out one flat face and you get 441π, still not 450.75π.

Concept

Total surface area counts every face a solid shows, flat as well as curved. Cutting a solid creates new flat faces, so the pieces together have more area than the whole.

Three perpendicular cuts through the centre make eight equal pieces. Each keeps 1⁄8 of the curved surface, 4πr² ÷ 8 = πr²⁄2, and meets each cutting plane in a quarter of a great circle, πr²⁄4.

Per piece: πr²⁄2 + 3 × πr²⁄4 = 5πr²⁄4.

The same curved-plus-flat count gives a hemisphere 3πr²: half of the sphere's 4πr² curved surface, plus one flat circle of πr².

Key facts

Curved surface area of a sphere: 4πr².
A cut through the centre exposes a great circle of area πr².
Total surface area of a hemisphere: 3πr² (2πr² curved + πr² flat).
Each of the eight equal pieces of a sphere has total surface area 5πr²⁄4.

Study next

Surface area gained when a cube is cut into smaller cubesTotal surface area of a solid hemisphere versus a hollow hemispherical bowlVolume of a hemisphere (2⁄3 πr³) and of one-eighth of a sphere (πr³⁄6)

Common traps

Counting only the curved surface, 220.5π, and forgetting the three flat faces the cuts expose.
Giving each flat face a half-circle: the other two cuts split each great circle into four, so each piece gets a quarter.

Here the cut is described in words and the flat faces must be pictured.

The same curved-plus-flat count, 3πr² for a hemisphere, decides 17 Sep 2025, 16:00, Quant Q.11 (a hemisphere and a cylinder of equal radii with equal total surface areas).

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 56 SSC CGL questions on it, every solved shift.