SSC CGL 2025 Tier-I · 23 September 2025, Shift 1 · Quantitative Aptitude · Question 8 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 rectangular park is 60m by 40m. A semicircular pond of diameter 40m is inside. What percent of the park's area does the pond occupy?

(a)33.3%
(b)26.18%
(c)28.35%
(d)31.42%

Answer

Why

Correct — B. Compare the pond's area with the park's.

Park area = 60 × 40 = 2,400 m²
Pond radius = 40 ÷ 2 = 20 m
Pond area = ½ × π × 20² = 200π ≈ 628.32 m²

Percentage = 628.32 ÷ 2,400 × 100 ≈ 26.18% → option (b)

Why the others are wrong

(a)
33.3% — 33.3% is about one-third of the park, 800 m². The semicircle covers 200π ≈ 628 m², about 172 m² less.
(c)
28.35% — 28.35% of 2,400 m² is about 680 m², some 52 m² more than the semicircle's 200π ≈ 628 m².
(d)
31.42% — 31.42% of the park is about 754 m², some 126 m² more than the semicircle's 200π ≈ 628 m².

Concept

A semicircle's area is half a circle's, πr²⁄2, with r half the given diameter.

The share of a region covered is part ÷ whole × 100, so here it is 200π ÷ 2,400 = π⁄12 ≈ 0.2618.

The pond fits: its 40 m diameter can lie along a side, and its 20 m height is less than both 40 m and 60 m.

26.18% comes from π ≈ 3.1416. With π = 22⁄7 the pond is 628.57 m² and the share is 26.19%, so the nearest option is still 26.18%.

Key facts

Area of a semicircle = πr²⁄2.
Radius = diameter ÷ 2, so a 40 m diameter gives r = 20 m.
π⁄12 ≈ 0.2618.

Study next

Area of a quadrant, πr²⁄4, inside a squareArea left over when a circle is cut from a rectanglePerimeter of a semicircle, πr + 2r

Common traps

Using the diameter as the radius: π × 40² ÷ 2 = 800π ≈ 2,513 m², more than the whole park.
Using the full circle: 400π ≈ 1,257 m² gives about 52.4%, which is not an option.

A part-of-the-whole area percentage is also asked at 21 Sep 2025, 16:00, Quant Q.8, where a triangle of 600 m² is 37.5% of a 1,600 m² triangle-plus-rectangle field.

Related PYQs

No directly related past PYQ was found.

Topic: Percentage — all 82 SSC CGL questions on it, every solved shift.