Mensuration: Quick & Simple Study Notes
(For AWS Certification – Quantitative Aptitude)
1. What is Mensuration?
Mensuration is the math for measuring parts of shapes.
- Perimeter – distance around a shape.
- Area – how much floor it covers.
- Volume – how much space a 3‑D shape holds.
- Surface Area – how much paint a shape needs.
2. 2‑D Shapes
| Shape | Perimeter | Area | Everyday Analogy | Tiny Example |
|---|---|---|---|---|
| Rectangle | (2,(L+W)) | (L\times W) | A TV screen | L = 4 m, W = 3 m → P = 14 m, A = 12 m² |
| Square | (4,s) | (s^2) | A chessboard | s = 2 m → P = 8 m, A = 4 m² |
| Triangle | (a+b+c) | (\frac{1}{2},base\timesheight) | A slice of pizza | base = 5 cm, height = 3 cm → A = 7.5 cm² |
| Circle | (2\pi r) | (\pi r^2) | A round plate | r = 6 cm → P ≈ 37.7 cm, A ≈ 113.1 cm² |
Tip:
- Draw the shape.
- Label the sides or radius.
- Plug numbers into the right formula.
3. 3‑D Shapes
| Shape | Surface Area (SA) | Volume (V) | Everyday Analogy | Tiny Example |
|---|---|---|---|---|
| Cube | (6,s^2) | (s^3) | A shoebox | s = 5 cm → SA = 150 cm², V = 125 cm³ |
| Rectangular Prism | (2(lw+wh+hl)) | (l\times w\times h) | A cereal box | l = 10 cm, w = 5 cm, h = 4 cm → SA = 260 cm², V = 200 cm³ |
| Sphere | (4\pi r^2) | (\frac{4}{3}\pi r^3) | A ball | r = 3 cm → SA ≈ 113.1 cm², V ≈ 113.1 cm³ |
| Cylinder | (2\pi r(h+r)) | (\pi r^2 h) | A can of soup | r = 2 cm, h = 5 cm → SA ≈ 87.96 cm², V ≈ 62.8 cm³ |
Remember:
Surface Area = total paint needed.
Volume = how many cubic units fit inside.
4. Quick Conversion Tricks
| Unit | 1 m² | 1 m³ |
|---|---|---|
| 1 square meter | 10 feet × 10 feet | – |
| 1 cubic meter | 1,000 liters | – |
| 1 square foot | 0.0929 m² | – |
| 1 cubic foot | 28.317 liters | – |
Why it matters:
AWS exam questions sometimes mix meters and feet.
Use the table to swap quickly.
5. Sample Practice Problems
| # | Problem | Answer |
|---|---|---|
| 1 | A rectangle has a length of 8 m and a width of 4 m. Find its perimeter and area. | P = 24 m, A = 32 m² |
| 2 | A cylinder has a radius of 3 cm and a height of 7 cm. Find its volume. | V ≈ 197 cm³ |
| 3 | A square’s perimeter is 48 cm. What is its area? | s = 12 cm → A = 144 cm² |
| 4 | A box (rectangular prism) measures 6 cm × 4 cm × 2 cm. Find its surface area. | SA = 104 cm² |
| 5 | A circle’s area is 78.5 cm². Find its radius. | r ≈ 5 cm (because (π r^2 = 78.5)) |
Tip:
Start by sketching the shape.
Label the unknown.
Choose the right formula.
Plug numbers, do the math.
6. Quick Review Checklist
- Know the basic formulas for perimeter, area, surface area, and volume.
- Practice converting units (meters ↔ feet, liters ↔ cubic meters).
- Sketch shapes before solving.
- Check your answer with a quick sanity check (e.g., area should be non‑negative).
Final Thought
Think of mensuration as counting the space a shape occupies or surrounds.
Just like a pizza shop wants to know how many slices fit on a pizza (area) and how much dough is needed for the crust (perimeter), you’ll use these formulas to solve AWS quantitative questions quickly.
Good luck!