SSC CGL 2025 Tier-I · 12 September 2025, Shift 3 · Quantitative Aptitude · Question 19 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 right circular cone has a radius of 7 cm and height of 24 cm. What is the slant height?

(a)25 cm
(b)30 cm
(c)35 cm
(d)40 cm

Answer

Why

Correct — A. The radius, the height and the slant height form a right triangle, with the slant height as the hypotenuse.

Square and add the legs: l² = r² + h²
= 7² + 24² = 49 + 576 = 625
Take the root: l = √625 = 25 cm → option (a)

Why the others are wrong

(b)
30 cm — 30² = 900, not 625. A 30 cm slant height with the same 24 cm height would need a radius of √(900 − 576) = 18 cm, not 7 cm.
(c)
35 cm — 35 cm is longer than 7 + 24 = 31 cm. The hypotenuse of a right triangle is always shorter than its other two sides added together, so it fails before any squaring.
(d)
40 cm — 40 cm is longer than 7 + 24 = 31 cm, so no right triangle with legs 7 and 24 can have it as the hypotenuse. Squaring agrees: 40² = 1600, not 625.

Concept

The apex of a right circular cone sits directly above the centre of its base. Cut the cone through that axis and you see a right triangle: the height and the radius are the legs, and the slant height is the hypotenuse.

So l = √(r² + h²) for every right circular cone.

7, 24 and 25 form a Pythagorean triple (49 + 576 = 625), so the root comes out whole.

A size check narrows it first: the slant height must be longer than the 24 cm height and shorter than r + h = 31 cm. That removes 35 cm and 40 cm, and squaring separates 25 cm from 30 cm.

Key facts

Slant height of a right circular cone: l = √(r² + h²).
7, 24, 25 is a Pythagorean triple: 7² + 24² = 25².
Curved surface area of a cone = πrl, so it uses the slant height, not the vertical height.

Study next

Curved and total surface area of a cone: πrl and πr(r + l)Volume of a cone, ⅓πr²h, which uses the vertical heightPythagorean triples such as 3-4-5, 5-12-13, 8-15-17 and 7-24-25

Common traps

Adding the legs, 7 + 24 = 31 cm. The slant height is √(7² + 24²), which is always shorter than that sum.
Mixing up h and l: the height runs from the apex straight down to the centre of the base, the slant height from the apex along the surface to the rim.

The same 7 cm by 24 cm cone appears at 15 Sep 2025, 12:30, Quant Q.16, where its 25 cm slant height is needed to find the radius of the inscribed sphere, 5.25 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.