SSC CGL 2024 Tier-I · 10 September 2024, Shift 2 · Quantitative Aptitude · Question 12 of 100

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 6 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

A right triangle with sides 3 cm, 4 cm and 5 cm is rotated about the sides of 3 cm to form a cone. The volume of the cone so formed is:

(a)25π cm
(b)28π cm
(c)20π cm
(d)16π cm

Answer

Why

Correct — D. Spinning a right triangle about one leg sweeps out a cone whose axis is that leg.

The rotation here is about the 3 cm side, so:
height h = 3 cm (the axis of rotation)
radius r = 4 cm (the other leg sweeps the base circle)
the 5 cm hypotenuse becomes the slant height and takes no part in the volume

Apply the cone formula:
Volume = ⅓ π r² h
= ⅓ × π × 4² × 3
= ⅓ × π × 16 × 3 = 16π → option (d).

Why the others are wrong

(a)
25π cm — 25π uses the hypotenuse as the radius: ⅓ π × 5² × 3 = 25π. The 5 cm side never touches the base circle — it sweeps the slanted surface, which is why it is the slant height.
(b)
28π cm — 28π is 16π + 12π, this cone plus the cone you get by spinning the same triangle about its 4 cm leg. No single rotation of this triangle produces it.
(c)
20π cm — 20π is the cone's curved surface area, π r l = π × 4 × 5, not its volume. Surface area is where the slant height belongs; volume needs ⅓ π r² h.

Concept

This is a solid of revolution. Spin a right triangle about one of its legs and you get a cone.

The leg you spin about becomes the height. The other leg sweeps out the base radius. The hypotenuse becomes the slant height, l.

So one 3-4-5 triangle gives two different cones. About the 3 cm leg: r = 4, h = 3, volume 16π cm³. About the 4 cm leg: r = 3, h = 4, volume 12π cm³.

The slant height governs surface area, never volume.

The options are printed as "16π cm" — the paper's own unit slip, since a volume is measured in cm³. The number is right and the unit is not, so do not let the printed unit argue you out of the correct option.

Key facts

Rotating a right triangle about a leg gives a cone whose height is that leg and whose base radius is the other leg.
Volume of a cone = ⅓ π r² h.
Spun about its 3 cm leg the 3-4-5 triangle gives 16π cm³, and spun about its 4 cm leg it gives 12π cm³.
Curved surface area of a cone = π r l, where l is the slant height.

Study next

Solids of revolution from a rectangle and from a semicircle, giving a cylinder and a sphereCone volume against curved and total surface area, and when the slant height is neededThe frustum formed by rotating a right trapezium about its perpendicular side

Common traps

Taking the 5 cm hypotenuse as the radius, which gives 25π.
Swapping the two legs and reporting 12π, the cone from the other rotation.
Computing π r l = 20π because the 5 cm side is sitting there asking to be used.

The difficulty is placed in the set-up, not the arithmetic — which leg is the axis decides everything, and the formula is then one line. Geometry also comes up in this shift at Quant Q.16, on an exterior angle, and Quant Q.23, on a chord in a circle (10 Sep 2024, 12:30 PM).

Related PYQs

No directly related past PYQ was found.