SSC CGL 2025 Tier-I · 19 September 2025, Shift 2 · Quantitative Aptitude · Question 12 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.

Where this paper and its answers come from

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.

If the curved surface area of a hemisphere is 154 cm² find its diameter.

(a)9.9 cm
(b)8.4 cm
(c)6.2 cm
(d)5.2 cm

Answer

Why

Correct — A.
Curved surface of a hemisphere = 2πr², half of a sphere's 4πr²
2 × 22⁄7 × r² = 154
44⁄7 × r² = 154

Divide: r² = 154 × 7⁄44 = 24.5
Square root: r = √24.5 ≈ 4.95 cm
Double for the diameter: d = 2 × 4.95 = 9.9 cm → option (a)

Why the others are wrong

(b)
8.4 cm — A diameter of 8.4 cm means r = 4.2 cm, and 2 × 22⁄7 × 4.2² = 110.88 cm². That is well short of the 154 cm² given.
(c)
6.2 cm — r = 3.1 cm gives a curved surface of about 60.4 cm² (2 × 22⁄7 × 9.61). To reach 154 cm² the radius has to be close to 5 cm.
(d)
5.2 cm — As a diameter, 5.2 cm means r = 2.6 cm and about 42.5 cm² of curved surface. Read as the radius, 5.2 cm gives about 170 cm², so it fits neither way.

Concept

A solid hemisphere has two surfaces: the curved dome, 2πr², and the flat circular base, πr². Together they make the total surface, 3πr².

"Curved surface area" means the dome alone, so the equation is 2πr² = 154.

The question asks for the diameter, so the last step doubles the radius.

The stem gives no value of π. With 22⁄7, r² = 24.5, and with 3.14, r² ≈ 24.52. Both give a diameter of 9.9 cm to one decimal place.

Key facts

Curved surface area of a hemisphere = 2πr²
Total surface area of a solid hemisphere = 3πr², the dome plus the flat circle πr²
Volume of a hemisphere = (2⁄3)πr³

Study next

Total surface area of a hemisphere and of a hollow hemispherical bowlVolume of a hemisphere, and items that equate it with a surface areaMelting a hemisphere and recasting it into smaller solids

Common traps

Using the total surface 3πr² when the stem says curved surface area
Stopping at the radius, 4.95 cm, when the question asks for the diameter
Expecting r = 7 because 22⁄7 × 7² = 154, which is a circle's area πr², not the curved surface 2πr²

17 Sep 2025, 16:00, Quant Q.11 needs the total surface instead: a hemisphere's 3πr² set equal to a cylinder's 2πr(r + h) gives h : r = 1 : 2.

17 Sep 2025, 09:00, Quant Q.11 sets the volume equal to four times the curved surface 2πr² and is keyed 12 cm.

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.