SSC CGL 2025 Tier-I · 17 September 2025, Shift 2 · Quantitative Aptitude · Question 13 of 99

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 hemispherical dome covers a circular area of diameter 20 m. What is the approximate curved surface area of this dome?

(a)628m²
(b)514m²
(c)408m²
(d)762m²

Answer

Why

Correct — A. The dome is the curved half of a sphere standing on a circle of diameter 20 m.

Halve the diameter: r = 20 ÷ 2 = 10 m
Curved surface of a hemisphere = 2πr²
Substitute: 2 × π × 10² = 200π

Take π ≈ 3.14: 200 × 3.14 = 628 m² → option (a)

Why the others are wrong

(b)
514m² — 514 ÷ 6.28 ≈ 81.8, so 514 m² is 2πr² for a radius of about 9 m. The dome stands on a 20 m circle, so r = 10 m and r² = 100.
(c)
408m² — 408 ÷ 6.28 ≈ 65, a radius near 8 m. With r = 10 m the curved surface is 200π ≈ 628 m², so 408 falls about 220 m² short.
(d)
762m² — 762 ÷ 6.28 ≈ 121, which fits a radius of about 11 m. The circle covered has a diameter of 20 m, so the radius is 10 m.

Concept

A solid hemisphere has two surfaces: the curved dome, 2πr², and the flat circular base, πr². A dome's roof is the curved surface alone, and that is what the question asks.

The circle the dome covers is its base, so the base diameter gives the radius directly: r = 10 m.

The word approximate is there because 200π is not a whole number: 200π ≈ 628.3 with π = 3.1416, and ≈ 628.6 with π = 22⁄7. Either way option (a) is the nearest value.

Key facts

Curved surface area of a hemisphere = 2πr².
Total surface area of a solid hemisphere = 3πr², the curved 2πr² plus the base πr².
A whole sphere's surface, 4πr², is double a hemisphere's curved surface.

Study next

Total surface area of a solid hemisphere, 3πr²Inner and outer surfaces of a hollow hemisphere or bowlCost of painting a dome at a given rate per m²

Common traps

Using 20 m as the radius: 2π × 400 ≈ 2,513 m².
Adding the base πr² ≈ 314 m² to give the total surface 942 m², when the dome's curved surface is asked.

Hemisphere surface formulas also decide 17 Sep 2025, 09:00, Quant Q.11, where the volume equals 4 × the curved surface: 2⁄3 π r³ = 8π r² gives r = 12 cm.

18 Sep 2025, 12:30, Quant Q.11 asks the total surface 3πr² of a hemisphere recast from two smaller ones.

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.