SSC CGL 2025 Tier-I · 14 September 2025, Shift 2 · Quantitative Aptitude · Question 20 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.

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.

A cone is such that the area of its base equals its lateral surface area. If radius is r, find the slant height l.

(a)r
(b)2r
(c)3r
(d)4r

Answer

Why

Correct — A. Write both areas with the same letters, then set them equal.

Base (a circle): area = πr²
Lateral (curved) surface: area = πrl
Set them equal: πr² = πrl
Divide both sides by πr: l = r → option (a)

Why the others are wrong

(b)
2r — l = 2r makes the curved surface πr × 2r = 2πr², twice the base area, not equal to it.
(c)
3r — l = 3r makes the curved surface πr × 3r = 3πr², three times the base area.
(d)
4r — l = 4r makes the curved surface 4πr². Any slant height longer than r gives a curved surface larger than the base.

Concept

A cone has two surfaces: the flat circular base, πr², and the curved or lateral surface, πrl, where l is the slant height from the rim to the tip.

Both share the factor πr, so comparing them reduces to comparing r with l. The curved surface equals the base when l = r and exceeds it whenever l > r.

Taken literally, the key describes a flattened cone. Slant height is √(r² + h²), so l = r forces the height to be h = 0. The question tests the two area formulas, and on those the algebra gives l = r.

Key facts

Curved (lateral) surface area of a cone = πrl.
Total surface area of a cone = πr² + πrl = πr(r + l).
Slant height l = √(r² + h²), so l is longer than r for any cone with height.

Study next

Total surface area of a cone, πr(r + l)A sector rolled into a cone, where the arc length becomes the base circumference 2πrCurved surface area of a frustum, π(R + r)l

Common traps

Putting the vertical height h into πrl in place of the slant height l.
Using the cylinder's 2πrh for the curved surface, which gives l = r⁄2 and matches no option.

18 Sep 2024, 12:30, Quant Q.23 asks for πrl directly: r = 9 cm and l = 49 cm, keyed 1386 cm².

12 Sep 2025, 16:00, Quant Q.19 asks for l itself from r = 7 cm and h = 24 cm, keyed 25 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 51 SSC CGL questions on it, every solved shift.