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CSAT · 20 questions

Geometry & mensuration

Every UPSC CSAT question on this topic, 2016–2026, newest first. Tap an option to check yourself; the answer and explanation open below it.

Geometry & mensuration questions per year: 2016: 6, 2017: 1, 2018: 3, 2019: 0, 2020: 3, 2021: 2, 2022: 2, 2023: 2, 2024: 1, 2025: 0, 2026: 0 Asked in 8 of 11 years · most in 2016 (6)
Timed · 30 minutes a set Practise Geometry & mensuration as timed tests 1 set of about 20 questions with UPSC's CSAT marking. Start practising

UPSC syllabus: “Basic numeracy (numbers and their relations, orders of magnitude, etc.) (Class X level), Data interpretation (charts, graphs, tables, data sufficiency etc. — Class X level);” Sub-topics in the detailed syllabus →

CSAT 2016 · Q39

Easy

टिन का एक टुकड़ा आयत की आकृति में है, जिसकी लम्बाई 12 सेमी तथा चौड़ाई 8 सेमी है। इसका उपयोग कर एक बन्द घन निर्मित किया जाता है। घन की भुजा की लम्बाई क्या है ?

Read this question in English

A piece of tin is in the form of a rectangle having length 12 cm and width 8 cm. This is used to construct a closed cube. The side of the cube is:

(a) 2 cm · (b) 3 cm · (c) 4 cm · (d) 6 cm

उत्तर और व्याख्या · explanation in English

Answer: (c) 4 सेमी

The whole sheet of 12 × 8 = 96 cm² becomes the surface of the cube. A closed cube has six square faces, so 6s² = 96, s² = 16 and each side is 4 cm.

  1. Area of the sheet = 12 × 8 = 96 cm².
  2. Closed cube: 6s² = 96, so s² = 16 and s = 4 cm.
  3. Check: 6 × 4 × 4 = 96.

Remember · Sheet-to-solid problems: the sheet's area equals the surface area of the solid made from it.

Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2016 · Q49

Easy

कोई व्यक्ति जमीन पर किसी बिंदु ‘O’ से सीधे रास्ते से उत्तर-पूर्व की दिशा में एक पहाड़ी पर चढ़ता है और 5 किमी. की दूरी तय करके बिंदु ‘A’ पर पहुंचता है। उसके बाद, वह बिंदु ‘A’ से उत्तर-पश्चिम की दिशा में बिंदु ‘B’ तक जाता है। AB की दूरी 12 किमी. है। अब वह व्यक्ति प्रारम्भिक बिंदु ‘O’ से कितनी दूर है ?

Read this question in English

A person climbs a hill in a straight path from point ‘O’ on the ground in the direction of north-east and reaches a point ‘A’ after travelling a distance of 5 km. Then, from the point ‘A’ he moves to point ‘B’ in the direction of north-west. Let the distance AB be 12 km. Now, how far is the person away from the starting point ‘O’?

(a) 7 km · (b) 13 km · (c) 17 km · (d) 11 km

उत्तर और व्याख्या · explanation in English

Answer: (b) 13 किमी.

North-east and north-west are at right angles, so the path turns through 90° at A. OB is the hypotenuse of a right triangle with arms 5 km and 12 km: √(5² + 12²) = 13 km.

  1. North-east and north-west are perpendicular, so angle OAB = 90°.
  2. OA = 5 km and AB = 12 km are the arms of the right angle.
  3. OB = √(5² + 12²) = √169 = 13 km.

Remember · Directions 90° apart (NE and NW, N and E) form a right angle — use Pythagoras; 5-12-13 is a triple worth knowing.

Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2016 · Q50

Easy

एक खेत आयताकार आकृति में है जिसकी लम्बाई X₁ मीटर और चौड़ाई X₂ मीटर है .(X₁ और X₂ चर हैं)। यदि X₁ + X₂ = 40 मीटर है तो उस खेत का क्षेत्रफल निम्नलिखित किस एक मान से अधिक नहीं होगा ?

Read this question in English

An agricultural field is in the form of a rectangle having length X₁ meters and breadth X₂ meters (X₁ and X₂ are variable). If X₁ + X₂ = 40 meters, then the area of the agricultural field will not exceed which one of the following values?

(a) 400 sq m · (b) 300 sq m · (c) 200 sq m · (d) 80 sq m

उत्तर और व्याख्या · explanation in English

Answer: (a) 400 वर्ग मीटर

When the length and breadth add up to 40 m, the area is greatest when the rectangle is a square of side 20 m. So the area can never exceed 20 × 20 = 400 sq m.

  1. For a fixed sum X₁ + X₂ = 40, the product X₁ × X₂ is largest when X₁ = X₂ = 20.
  2. Maximum area = 20 × 20 = 400 sq m.
  3. Check: 19 × 21 = 399 and 10 × 30 = 300, both below 400.

Remember · For a fixed sum, a product is largest when the parts are equal.

Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2016 · Q57

Easy

AB किसी विशाल वृक्ष का उर्ध्वाधर तना है और A वह बिंदु है जहाँ पर तने का आधार जमीन को छूता है। किसी तूफ़ान के कारण तना उस बिंदु C पर टूट गया है जो 12 मीटर की ऊंचाई पर है। टूटा हुआ भाग आंशिक रूप से तने के ऊर्ध्वाधर हिस्से से C पर जुड़ा है। यदि टूटे हुए भाग का सिरा B, जमीन को D पर छूता है जो बिंदु A से 5 मीटर की दूरी पर है, तो तने की मूल ऊंचाई क्या है ?

Read this question in English

AB is a vertical trunk of a huge tree with A being the point where the base of the trunk touches the ground. Due to a cyclone, the trunk has been broken at C which is at a height of 12 meters, broken part is partially attached to the vertical portion of the trunk at C. If the end of the broken part B touches the ground at D which is at a distance of 5 meters from A, then the original height of the trunk is:

(a) 20 m · (b) 25 m · (c) 30 m · (d) 35 m

उत्तर और व्याख्या · explanation in English

Answer: (b) 25 मीटर

The standing 12 m of trunk and the 5 m along the ground form a right triangle whose hypotenuse is the broken part: √(12² + 5²) = 13 m. The original height was 12 + 13 = 25 m.

  1. AC = 12 m (standing), AD = 5 m (on the ground), angle CAD = 90°.
  2. Broken part CD = √(12² + 5²) = √169 = 13 m.
  3. Original height = AC + CB = 12 + 13 = 25 m.

Remember · Broken-tree problems: original height = standing part + hypotenuse from the break to where the top touches the ground.

Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2016 · Q59

Easy

किसी घन (क्यूब) के सभी फलक विभिन्न रंगों से रंगे गए हैं। उसे समान आमाप के छोटे-छोटे घनों में इस प्रकार काटा गया कि छोटे घन की भुजा बड़े घने की एक चौथाई हो। केवल एक ही रंगे हुए फलक वाले छोटे घनों की संख्या संख्या कितनी होगी ?

Read this question in English

A cube has all its faces painted with different colours. It is cut into smaller cubes of equal sizes such that the side of the small cube is one-fourth the big cube. The number of small cubes with only one of the sides painted is:

(a) 32 · (b) 24 · (c) 16 · (d) 8

उत्तर और व्याख्या · explanation in English

Answer: (b) 24

Each edge of the big cube is cut into 4, so every face is a 4 × 4 grid of small cubes. Only the inner 2 × 2 on each face has exactly one painted side: 6 × 4 = 24.

  1. The big cube becomes 4 × 4 × 4 = 64 small cubes.
  2. On each face, the cubes painted on that face alone form the inner (4 − 2) × (4 − 2) = 4.
  3. Six faces: 6 × 4 = 24.

Remember · Cube cut into n per edge: one face painted = 6(n − 2)², two faces = 12(n − 2), three faces = 8.

Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2016 · Q73

Easy

एक बेलनाकार ओवरहैड टंकी को, जिसकी त्रिज्या 2 मी और ऊंचाई 7 मी है, 5.5 मी × 4 मी × 6 मी माप वाली किसी भूमिगत टंकी के जल से भरा जाना है। ओवरहैड टंकी को पूरा भर देने के बाद, भूमिगत टंकी का कितना भाग पानी से भरा है ?

Read this question in English

A cylindrical overhead tank of radius 2 m and height 7 m is to be filled from an underground tank of size 5.5 m × 4 m × 6 m. How much portion of the underground tank is still filled with water after filling the overhead tank completely?

(a) 1/3 · (b) 1/2 · (c) 1/4 · (d) 1/6

उत्तर और व्याख्या · explanation in English

Answer: (a) 1/3

The cylinder holds 22/7 × 2² × 7 = 88 m³, and the full underground tank holds 5.5 × 4 × 6 = 132 m³. After the cylinder is filled, 44 m³ remain — one-third of the underground tank.

  1. Overhead tank: πr²h = 22/7 × 2 × 2 × 7 = 88 m³.
  2. Underground tank (taken as full at the start): 5.5 × 4 × 6 = 132 m³.
  3. Left: 132 − 88 = 44 m³, and 44/132 = 1/3.

Remember · When 7 appears in a radius or height, take π = 22/7; the numbers are usually set to cancel neatly.

Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

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