SSC CGL 2025 Tier-I · 23 September 2025, Shift 3 · Quantitative Aptitude · Question 4 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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A spherical tank is filled with water. The radius of the sphere is 6 meters. The tank is used to fill cylindrical containers, each with a radius of 1 meter and a height of 12 meters. How many containers can be filled?

(a)14
(b)18
(c)24
(d)30

Answer

Why

Correct — C. The sphere's water is shared among the cylinders, so divide one volume by the other.

Volume of sphere = 4⁄3 π r³ = 4⁄3 π × 6³
= 4⁄3 π × 216 = 288π m³
Volume of one cylinder = π r² h = π × 1² × 12 = 12π m³
Number of containers = 288π ÷ 12π = 24 → option (c)

Why the others are wrong

(a)
14 — 14 containers hold only 14 × 12π = 168π m³, leaving 120π m³ of the sphere's 288π m³ still in the tank.
(b)
18 — 18 comes from dropping the 4⁄3 in the sphere's volume: π × 216 ÷ 12π = 18. The full volume is 288π m³, not 216π m³.
(d)
30 — 30 containers need 30 × 12π = 360π m³, more water than the 288π m³ the sphere holds.

Concept

When liquid is poured from one vessel into others, volume is conserved: the volume poured out equals the number of containers × the volume of one.

Sphere: V = 4⁄3 π r³. Cylinder: V = π r² h. Both formulas carry π, so it cancels in the division. Never multiply out 3.14 or 22⁄7 first.

The division comes out to exactly 24, so there is no leftover water. When it does not divide evenly, count only the containers that are completely filled.

Key facts

Volume of a sphere = 4⁄3 π r³.
Volume of a cylinder = π r² h.
6³ = 216, and 4⁄3 × 216 = 288.
Containers filled = volume available ÷ volume of one container.

Study next

Melting and recasting a sphere into cones, wires or smaller spheresRise in water level when a solid is immersed in a cylinderVolumes of a hemisphere (2⁄3 π r³) and a cone (1⁄3 π r² h)

Common traps

Dropping the 4⁄3 in the sphere's volume, which gives 216π ÷ 12π = 18.
Squaring the sphere's radius instead of cubing it: 4⁄3 π × 36 = 48π, enough for only 4 containers.

Here the whole tank is poured into identical cylinders. Equating a spherical volume with a cylindrical one also decides 12 Sep 2025, 16:00, Quant Q.24, where a hemispherical stone of radius 7 cm raises the oil in a cylinder by 3 cm.

At 17 Sep 2025, 12:30, Quant Q.12 a ball of radius 4 cm displaces 256⁄3 π cm³ of water.

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.