SSC CGL 2025 Tier-I · 17 September 2025, Shift 1 · Quantitative Aptitude · Question 11 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.

The volume of a hemisphere is numerically equal to four times its curved surface area. Find its radius.

(a)12 cm
(b)15 cm
(c)16 cm
(d)17cm

Answer

Why

Correct — A.
Volume of a hemisphere = (2⁄3)πr³
Curved surface area = 2πr²

Set volume = 4 × curved surface area:
(2⁄3)πr³ = 4 × 2πr² = 8πr²
Divide both sides by πr²: (2⁄3)r = 8
r = 8 × 3⁄2 = 12 cm → option (a)

Why the others are wrong

(b)
15 cm — At r = 15, volume ÷ curved area = r⁄3 = 5, so the volume would be five times the curved area, not four.
(c)
16 cm — At r = 16, volume ÷ curved area = 16⁄3 ≈ 5.33, not 4. The ratio grows with r, and it equals 4 at r = 12.
(d)
17cm — At r = 17, volume ÷ curved area = 17⁄3 ≈ 5.67, not 4. Setting r⁄3 = 4 fixes r = 12.

Concept

For a hemisphere, volume ÷ curved surface area = (2⁄3)πr³ ÷ 2πr² = r⁄3. So "volume is k times the curved area" means r = 3k at once: here k = 4 and r = 12.

"Numerically equal" is there because cm³ and cm² cannot be equal as quantities. Only the numbers are compared, and they agree at one radius.

The question says curved surface area, 2πr². The total surface area of a solid hemisphere is 3πr², because it adds the flat face πr².

Using 3πr² gives (2⁄3)r = 12 and r = 18, which is not among the options.

Key facts

Volume of a hemisphere = (2⁄3)πr³.
Curved surface area of a hemisphere = 2πr².
Total surface area of a solid hemisphere = 3πr² (curved 2πr² plus the flat face πr²).
For a hemisphere, volume ÷ curved surface area = r⁄3.

Study next

A sphere whose volume is a multiple of its surface area: (4⁄3)πr³ ÷ 4πr² is also r⁄3Hemisphere against cylinder of the same radius: equal volumes or equal surface areasCurved against total surface area for the hemisphere, cylinder and cone

Common traps

Using the total surface area 3πr² when the question says curved surface area 2πr².
Using the sphere's volume (4⁄3)πr³ for a hemisphere: that gives (4⁄3)r = 8 and r = 6, not an option.

Hemisphere formulas are set against a cylinder's at 17 Sep 2025, 16:00, Quant Q.11 (equal total surface areas, keyed h : r = 1:2, option a) and 15 Sep 2025, 09:00, Quant Q.16 (equal volumes, keyed radius 18 cm, option d).

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.