Mensuration
वर्ष-वार विश्लेषण
पूछे जाने वाले प्रश्न प्रकार
PYQ से महत्वपूर्ण तथ्य
The volume of a cube with side 5 cm is:
125 cm³
A cuboid has dimensions 12cm, 8cm, 6cm. Surface area is:
432 sq.cm
Assertion: Wheel makes 1000 revolutions in 88km. Reason: Radius is 14 meters.
Both correct, R explains A
A rectangle has length 12 cm and breadth 8 cm. What is its area?
96 cm²
What is the area of a circle with radius 7 cm? (π = 22/7)
154 cm²
A cylinder has radius 7 cm and height 10 cm. What is its volume? (π = 22/7)
1540 cm³
अध्ययन नोट्स
2D Figures — Area and Perimeter formulas: Rectangle: A = l×b, P = 2(l+b). Square: A = s², P = 4s. Triangle: A = ½×b×h, A = √[s(s-a)(s-b)(s-c)] (Heron's formula where s = semi-perimeter). Circle: A = πr², C = 2πr. Parallelogram: A = b×h. Trapezium: A = ½×(a+b)×h (where a,b are parallel sides). Rhombus: A = ½×d₁×d₂ (product of diagonals).
3D Figures — Volume formulas (match-the-following favorite): Cuboid = L×B×H, Cube = a³, Cylinder = πr²h, Cone = (1/3)πr²h, Sphere = (4/3)πr³, Hemisphere = (2/3)πr³. Surface area formulas: Cuboid TSA = 2(lb+bh+hl), Cylinder TSA = 2πr(r+h), Cone TSA = πr(r+l) where l = slant height = √(r²+h²), Sphere TSA = 4πr².
Wheel/rotation problems: Circumference = 2πr = πd. If wheel makes n revolutions to cover distance d, then: 2πr × n = d. Example: Wheel makes 1000 revolutions in 88 km → circumference = 88000/1000 = 88m → 2×(22/7)×r = 88 → r = 14m. These problems require careful unit conversion (km to m).
Compound Interest vs Simple Interest: CI-SI difference for 2 years: Difference = P(r/100)². Example: P=18000, difference=405 → (r/100)² = 405/18000 = 0.0225 → r/100 = 0.15 → r = 15%. For 3 years: Difference = P(r/100)² × (3 + r/100). SI = PRT/100. CI = P(1+r/100)ⁿ - P.
REET Exam Tips: 6 questions — mostly volume formula matching and word problems. Focus on: Volume formulas (Cone = 1/3 of Cylinder, Hemisphere = 2/3 of Sphere), wheel circumference problems, and CI-SI difference formula for 2 years. Practice unit conversions carefully.