Mensurationक्षेत्रमितिquestions and answersप्रश्न और उत्तर
Mensuration is formula-heavy, so it rewards a good formula sheet and careful units. SSC asks it in almost every paper.
Unlimitedअसीमितfresh questionsनए प्रश्न
Answersउत्तरalways one tap awayहमेशा एक टैप दूर
2subtopicsउप-टॉपिक
SSC CGL ~3
IBPS PO ~1
Practice questions are in English for now.अभ्यास के प्रश्न अभी अंग्रेज़ी में हैं।
How mensuration worksक्षेत्रमिति को समझिए
For paths around or inside a field, find the outer area minus the inner area. Paths through the middle overlap at the crossing, so subtract the overlap once.
For solids, check whether the question wants the curved surface, the total surface, or the volume. Painting is surface area; filling is volume.
Take π = 22/7 when the numbers are multiples of 7; it keeps the arithmetic clean.
Each trick says when to use it, why it works and when it fails. Formula tricks are checked by code over their whole range.हर ट्रिक बताती है कि उसे कब इस्तेमाल करें, वह क्यों काम करती है और कब नहीं। सूत्र वाली ट्रिक्स को कोड से उनकी पूरी रेंज पर जाँचा गया है।
Mental mathsमानसिक गणित✓ Checked on 598 cases✓ 598 मामलों पर जाँची गई
Square from a neighbour you know
Use it when:कब इस्तेमाल करें: Squaring a number next to one you already know (41, 49, 51, 99).
n² = (n − 1)² + (n − 1) + n, or going down: n² = (n + 1)² − (n + 1) − n.
For two numbers equally far from a round one: (a + d)(a − d) = a² − d².
Exampleउदाहरण
41² and 47 × 53
→ 1600 + 40 + 41 = 1681; 2500 − 9 = 2491
Why it works, and when it failsयह क्यों काम करती है, और कब नहीं
Why:क्यों: n² − (n − 1)² = 2n − 1 = (n − 1) + n, and (a + d)(a − d) = a² − d².
Limits:सीमाएँ: Always true; it is fastest when the neighbour is a round number.
Mental mathsमानसिक गणित✓ Checked on 7 cases✓ 7 मामलों पर जाँची गई
Five triples that solve most direction questions
Use it when:कब इस्तेमाल करें: The final distance in a direction-sense question, or a right-triangle side.
Memorise 3-4-5, 5-12-13, 8-15-17, 7-24-25 and 20-21-29, plus their multiples (6-8-10, 9-12-15).
Exampleउदाहरण
Walks 6 km north, then 8 km east. Distance from start?
→ 6-8-10 → 10 km
Why it works, and when it failsयह क्यों काम करती है, और कब नहीं
Why:क्यों: These are the smallest whole-number solutions of a² + b² = c², and examiners pick them so the answer is a whole number.
Limits:सीमाएँ: Other cases need √(a² + b²); check whether the options are given in surd form.
Solved examplesहल किए गए उदाहरण
Answers and full solutions are shown. Hide them to test yourself first.उत्तर और पूरे हल दिखाए गए हैं। पहले खुद को परखने के लिए इन्हें छिपाइए।
Example 1उदाहरण 1 · Mensuration 2D: area, perimeter and paths · Easyआसान
A rectangular farm in Punjab is 20 m long and 16 m wide. Find the cost of fencing it at ₹16 per metre.
₹922
₹1,152
₹1,382
₹1,440
Answer:उत्तर:₹1,152
Perimeter = 2(20 + 16) = 72 m.
Cost = 72 × 16 = ₹1,152.
Example 2उदाहरण 2 · Mensuration 3D: volume and surface area · Easyआसान
A wooden box is 10 cm long, 12 cm wide and 6 cm high. Find its total surface area (in cm²).
403
504
554
630
Answer:उत्तर:504
TSA = 2(120 + 72 + 60) = 504 cm².
Example 3उदाहरण 3 · Mensuration 2D: area, perimeter and paths · Mediumमध्यम
A circular park in Bengaluru has a radius of 21 m. Find its circumference (in m). (Use π = 22/7)
99
106
132
158
Answer:उत्तर:132
Circumference = 2 × 22/7 × 21 = 132 m.
Example 4उदाहरण 4 · Mensuration 3D: volume and surface area · Mediumमध्यम
A cylindrical water tank in a village has radius 7 m and height 10 m. Find its curved surface area (in m²). (π = 22/7)
350
400
440
530
Answer:उत्तर:440
CSA = 2 × 22/7 × 7 × 10 = 440 m².
Example 5उदाहरण 5 · Mensuration 2D: area, perimeter and paths · Hardकठिन
A rectangular lawn 32 m × 10 m has a path 1 m wide all around it on the outside. Find the cost of paving the path at ₹20 per m².
₹1,320
₹1,760
₹1,940
₹2,110
Answer:उत्तर:₹1,760
Outer area = 34 × 12 = 408 m².
Lawn = 320 m². Path = 88 m².
Cost = 88 × 20 = ₹1,760.
Example 6उदाहरण 6 · Mensuration 3D: volume and surface area · Hardकठिन
Find the volume (in cm³) of a metal ball of radius 21 cm. (π = 22/7, answer to 2 decimal places if needed)
31,046
34,927
38,808
42,689
Answer:उत्तर:38,808
V = 4/3 × 22/7 × 9261
= 38,808 cm³.
Common mistakesआम गलतियाँ
Counting the crossing square of two paths twice.
Mixing curved and total surface area.
Forgetting to convert cm to m (and cm³ to litres: 1000 cm³ = 1 litre).
Frequently asked questionsअक्सर पूछे जाने वाले प्रश्न
Which mensuration formulas are most important for SSC?
Circle, triangle, cuboid, cylinder, cone and sphere formulas, plus area of paths and borders.
When should I use π = 22/7?
When the radius or diameter is a multiple of 7.
What is the difference between CSA and TSA?
CSA is only the curved side; TSA adds the flat ends.