Mensuration Formulas
⚡ Mensuration Formulas – 2-Minute Revision
🔢 2-D Figures (Perimeter P, Area A)
| Figure | P / A | Key Formula | Memory Hook |
|---|---|---|---|
| Square (side a) | P = 4a, A = a² | “4 walls, 1 floor” | |
| Rectangle (l,b) | P = 2(l+b), A = lb | “2 long, 2 short” | |
| Triangle (a,b,c) | P = a+b+c, A = ½×b×h | “Half base times height – always right” | |
| Equilateral Δ (side a) | A = (√3/4)a² | “Root-3 quarter” | |
| Circle (r) | C = 2πr, A = πr² | “Two pie are, pie are squared” | |
| Semi-circle | C = πr+2r, A = ½πr² | “Half pie + diameter” |
🔩 3-D Solids (Volume V, Surface Area S, Lateral L)
| Solid | V | Total S | Lateral L | Trick |
|---|---|---|---|---|
| Cuboid (l,b,h) | lbh | 2(lb+bh+hl) | 2h(l+b) | “L-B-H, wrap gift paper” |
| Cube (a) | a³ | 6a² | 4a² | “6 faces, 4 walls” |
| Cylinder (r,h) | πr²h | 2πr(r+h) | 2πrh | “πr²h – cake tin” |
| Cone (r,h) | (1/3)πr²h | πr(r+l) | πrl | “1/3 of cylinder, l=√(r²+h²)” |
| Sphere (r) | (4/3)πr³ | 4πr² | — | “4/3 & 4 – both 4” |
| Hemisphere | (2/3)πr³ | 3πr² | 2πr² | “Half sphere keeps 3π” |
🧠 Super-Mnemonics
- CSA cone: “πrl = pi-rol” (like a roll)
- Diagonal cuboid: √(l²+b²+h²) → “LBH—Long Big Height”
- Frustum: V = (πh/3)(R²+Rr+r²) → “h by 3, R-R-r”
📏 Quick Comparison Table (Cube vs Cuboid)
| Parameter | Cube (a) | Cuboid (l,b,h) |
|---|---|---|
| V | a³ | lbh |
| S | 6a² | 2(lb+bh+hl) |
| Diagonal | a√3 | √(l²+b²+h²) |
🚀 10 Rapid-Fire MCQs
-
The area of a semi-circle of diameter 14 cm is
a) 154 cm² b) 77 cm² c) 308 cm² d) 49 cm² -
Volume of a sphere of radius 3 cm (π=22/7) is nearest to
a) 113 cm³ b) 108 cm³ c) 123 cm³ d) 131 cm³ -
Lateral surface area of a cube of side 5 cm is
a) 125 cm² b) 150 cm² c) 100 cm² d) 75 cm² -
A cylinder has r=7 cm, h=10 cm. Its CSA is
a) 220 cm² b) 440 cm² c) 1540 cm² d) 3080 cm² -
The diagonal of a cuboid 3×4×12 cm is
a) 12 cm b) 13 cm c) 14 cm d) 15 cm -
Area of equilateral triangle of side 8 cm is
a) 16√3 cm² b) 32√3 cm² c) 64√3 cm² d) 24 cm² -
Volume of a cone is 100π cm³ and r=5 cm; its height is
a) 12 cm b) 10 cm c) 15 cm d) 20 cm -
Total surface area of hemisphere of radius 7 cm is
a) 308 cm² b) 462 cm² c) 616 cm² d) 154 cm² -
Perimeter of a sector with radius 7 cm & angle 90° is
a) 25 cm b) 11 cm c) 22 cm d) 14 cm -
If diagonal of square is 10√2 cm, its area is
a) 100 cm² b) 50 cm² c) 200 cm² d) 150 cm²
BETA
