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Master Geometry & Mensuration with this comprehensive study guide designed specifically for CHSL aspirants. This guide covers key concepts, shortcuts, and includes 10 practice MCQs to test your understanding.
Mensuration questions appear in almost every exam. Mastering area, perimeter, volume, and surface area formulas is essential.
| Shape | Area | Perimeter |
|---|---|---|
| Rectangle | l × b | 2(l+b) |
| Square | a² | 4a |
| Triangle | ½ × b × h | a+b+c |
| Circle | πr² | 2πr |
| Trapezium | ½(a+b)h | a+b+c+d |
| Rhombus | ½×d1×d2 | 4a |
| Shape | Volume | Surface Area |
|---|---|---|
| Cube | a³ | 6a² |
| Cuboid | l×b×h | 2(lb+bh+lh) |
| Cylinder | πr²h | 2πr(r+h) |
| Sphere | 4/3 πr³ | 4πr² |
| Cone | 1/3 πr²h | πr(r+l) where l=slant height |
Test your understanding with these 10 targeted MCQs based on the concepts above.
Q1. The area of a circle with radius 7 cm is: (π = 22/7)
Correct Answer: A
Area = πr² = (22/7) × 7 × 7 = 22 × 7 = 154 cm².
Q2. Find the volume of a cube with side 5 cm.
Correct Answer: C
Volume of cube = a³ = 5³ = 5 × 5 × 5 = 125 cm³.
Q3. The perimeter of a rectangle is 56 cm. If the length is 18 cm, find the breadth.
Correct Answer: B
Perimeter = 2(l+b). 56 = 2(18+b). 28 = 18+b. b = 10 cm.
Q4. A right triangle has legs 6 cm and 8 cm. Find the hypotenuse.
Correct Answer: B
Using Pythagoras: c² = 6² + 8² = 36 + 64 = 100. c = 10 cm. (This is a 6-8-10 = 3-4-5 triple × 2)
Q5. The area of an equilateral triangle with side 4 cm is:
Correct Answer: A
Area = (√3/4) × a² = (√3/4) × 16 = 4√3 cm².
Q6. Volume of a cylinder with radius 7 cm and height 10 cm is:
Correct Answer: B
V = πr²h = (22/7) × 7² × 10 = (22/7) × 49 × 10 = 22 × 7 × 10 = 1540 cm³.
Q7. The diagonal of a square is 10√2 cm. What is its area?
Correct Answer: B
Diagonal of square = a√2. So a√2 = 10√2, a = 10 cm. Area = a² = 100 cm².
Q8. A rhombus has diagonals 12 cm and 16 cm. Find its area.
Correct Answer: C
Area of rhombus = (d1 × d2)/2 = (12 × 16)/2 = 192/2 = 96 cm².
Q9. Total surface area of a sphere with radius 3.5 cm is: (π = 22/7)
Correct Answer: A
TSA = 4πr² = 4 × (22/7) × (3.5)² = 4 × (22/7) × 12.25 = 4 × 38.5 = 154 cm².
Q10. The volume of a cone with radius 6 cm and height 7 cm is: (π = 22/7)
Correct Answer: A
V = (1/3)πr²h = (1/3) × (22/7) × 36 × 7 = (1/3) × 22 × 36 = 22 × 12 = 264 cm³.
