SSC CGL 2025 Tier-I · 16 September 2025, Shift 1 · Quantitative Aptitude · Question 14 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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If the radius of a sphere is increased to twice its original size, what is the ratio of the new surface area to the original surface area, as well as the proportion of the new volume to the original volume?

(a)4:1 and 2:1
(b)4:1 and 8:1
(c)8:1 and 4:1
(d)2:1 and 4:1

Answer

Why

Correct — B. Surface area grows with r² and volume with r³, so raise the radius factor to each power.

Radius factor: r → 2r, factor 2
Surface area 4πr²: factor 2² = 4, ratio 4 : 1
Volume 4⁄3 πr³: factor 2³ = 8, ratio 8 : 1
Pair: 4 : 1 and 8 : 1 → option (b)

Why the others are wrong

(a)
4:1 and 2:1 — The volume part is wrong: 2 : 1 treats volume as growing with r. Volume is 4⁄3 πr³, so doubling r multiplies it by 2³ = 8.
(c)
8:1 and 4:1 — The two ratios are swapped. Surface area carries r² (factor 4) and volume carries r³ (factor 8), so the pair reads 4 : 1 then 8 : 1.
(d)
2:1 and 4:1 — Both exponents are one too low: 2 : 1 for area treats it as growing with r, and 4 : 1 for volume treats it as growing with r². The true factors are 2² and 2³.

Concept

When every length of a solid scales by k, its surface area scales by k² and its volume by k³. Area is length × length; volume is length × length × length.

A sphere has one length, its radius, so doubling the radius gives k = 2: surface area × 4, volume × 8.

Check with numbers. Take r = 1 and r = 2.
Surface area: 4π(1)² = 4π and 4π(2)² = 16π, ratio 4 : 1
Volume: 4⁄3 π(1)³ = 4⁄3 π and 4⁄3 π(2)³ = 32⁄3 π, ratio 8 : 1

Key facts

Surface area of a sphere = 4πr².
Volume of a sphere = 4⁄3 πr³.
Scaling all lengths by k multiplies area by k² and volume by k³.

Study next

Percentage change in a sphere's surface area and volume when the radius changes by x%Volume change of a cone or cylinder when radius and height change by different factorsRatio of radii from a given ratio of volumes (cube root)

Common traps

Swapping the pair — the question asks for surface area first, then volume.
Treating volume as doubling because the radius doubled.

Scaling by powers of the factor also decides 17 Sep 2025, 09:00, Quant Q.13: a cone's height tripled and radius halved changes its volume by 3 × (1⁄2)² = 3⁄4 of the original.

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.