📏 Class 8 CBSE – Mensuration
“How big is something? How much space does it occupy?”
Mensuration is the part of maths that helps you measure areas and volumes of everyday objects – from the floor in your room to the water inside a bottle.
1️⃣ What is Mensuration?
- Area = how much surface a 2‑D shape covers.
- Volume = how much space a 3‑D shape occupies.
Think of a rectangle as a flat piece of paper.
Think of a cube as a shoebox.
2️⃣ Units of Measurement
| Quantity | Unit (SI) | Example |
|---|---|---|
| Length | cm, m | 1 m = 100 cm |
| Area | cm², m² | 1 m² = 10 000 cm² |
| Volume | cm³, m³ | 1 m³ = 1 000 000 cm³ |
Tip: Always keep the unit the same when you multiply or divide.
3️⃣ Area of 2‑D Shapes
| Shape | Everyday Analogy | Formula | Tiny Example |
|---|---|---|---|
| Rectangle | Floor tiles | (A = l \times w) | 5 m × 3 m → (A = 5 \times 3 = 15) m² |
| Square | Picture frame | (A = s^2) | 4 m → (A = 4^2 = 16) m² |
| Triangle | Pizza slice | (A = \frac{1}{2} \times b \times h) | base = 6 m, height = 4 m → (A = \frac{1}{2}\times6\times4 = 12) m² |
| Circle | Wheel | (A = \pi r^2) | radius = 2 m → (A \approx 3.14 \times 4 = 12.56) m² |
| Parallelogram | Tilted lid | (A = b \times h) | base = 5 m, height = 3 m → (A = 15) m² |
| Trapezium (Trapezoid) | Stairs board | (A = \frac{1}{2} (a + b) \times h) | bases 8 m & 4 m, height 3 m → (A = 0.5 \times 12 \times 3 = 18) m² |
| Ellipse | Oval pond | (A = \pi a b) | semi‑axes 5 m & 3 m → (A \approx 3.14 \times 15 = 47.1) m² |
Note: The height (h) is the perpendicular distance between the two bases in a trapezium.
4️⃣ Volume of 3‑D Shapes
| Shape | Everyday Analogy | Formula | Tiny Example |
|---|---|---|---|
| Cube | Crate | (V = s^3) | side = 2 m → (V = 8) m³ |
| Cuboid | Mattress | (V = l \times w \times h) | 2 m × 1.5 m × 0.9 m → (V = 2.7) m³ |
| Sphere | Ball | (V = \frac{4}{3}\pi r^3) | radius = 1 m → (V \approx 4.19) m³ |
| Cylinder | Water bottle | (V = \pi r^2 h) | radius = 0.5 m, height = 2 m → (V \approx 1.57) m³ |
| Cone | Ice‑cream cone | (V = \frac{1}{3}\pi r^2 h) | radius = 0.3 m, height = 0.8 m → (V \approx 0.25) m³ |
| Prism | Box with slanted top | (V = A_{\text{base}} \times h) | base area = 4 m², height = 3 m → (V = 12) m³ |
| Pyramid | Egyptian temple | (V = \frac{1}{3} A_{\text{base}} \times h) | base area = 9 m², height = 6 m → (V = 18) m³ |
Quick tip: For any prism or pyramid, first find the area of its base, then multiply by the height (and divide by 3 for pyramids).