Maths Made Easy
Mensuration Formulas for Class 8–10 (All Shapes, Area & Volume)
2026-11-07 · 7 min read
Mensuration Formulas for Class 8–10 (All Shapes, Area & Volume)
Mensuration — finding the area, perimeter, surface area and volume of shapes — runs through Class 8, 9 and 10 maths. Here is every formula a student needs, in one printable reference.
2D Shapes: Area & Perimeter
| Shape | Area | Perimeter |
|---|---|---|
| Square (side a) | a² | 4a |
| Rectangle (length l, breadth b) | l × b | 2(l + b) |
| Triangle (base b, height h) | ½ × b × h | Sum of all three sides |
| Circle (radius r) | πr² | 2πr (circumference) |
| Parallelogram (base b, height h) | b × h | 2(a + b), a = slant side |
| Rhombus (diagonals d₁, d₂) | ½ × d₁ × d₂ | 4 × side |
| Trapezium (parallel sides a, b, height h) | ½ × (a + b) × h | Sum of all four sides |
3D Shapes: Surface Area & Volume
| Shape | Curved/Lateral Surface Area | Total Surface Area | Volume |
|---|---|---|---|
| Cube (side a) | 4a² (4 side faces) | 6a² | a³ |
| Cuboid (l, b, h) | 2h(l + b) | 2(lb + bh + hl) | l × b × h |
| Cylinder (radius r, height h) | 2πrh | 2πr(r + h) | πr²h |
| Cone (radius r, height h, slant l) | πrl | πr(r + l) | ⅓ × πr²h |
| Sphere (radius r) | — | 4πr² | 4/3 × πr³ |
| Hemisphere (radius r) | 2πr² | 3πr² | 2/3 × πr³ |
Good to know: a cone's slant height l is found using l² = r² + h² (Pythagoras on the cone's cross-section) — it is not the same as the vertical height h.
Worked Example
Find the volume and total surface area of a cone with radius 7 cm and height 24 cm. (Use π = 22/7.)
Slant height: l = √(r² + h²) = √(49 + 576) = √625 = 25 cm.
Volume = ⅓ × π × r² × h = ⅓ × 22/7 × 49 × 24 = 1232 cm³.
Total surface area = πr(r + l) = 22/7 × 7 × (7 + 25) = 22 × 32 = 704 cm².
Frequently Asked Questions
What is the difference between surface area and volume?
Surface area measures the total area covering the outside of a 3D shape (in square units); volume measures the space it occupies inside (in cubic units).
What is the formula for the slant height of a cone?
l = √(r² + h²), where r is the base radius and h is the vertical height.
Why does a cube have two different surface area values (4a² and 6a²)?
4a² is the lateral (side-only) surface area of just the four vertical faces; 6a² is the total surface area including the top and bottom faces too.
Mensuration Formulas for Class 8–10 (All Shapes, Area & Volume) — FAQs
What is the difference between surface area and volume?
Surface area measures the total area covering the outside of a 3D shape (in square units); volume measures the space it occupies inside (in cubic units).
What is the formula for the slant height of a cone?
l = √(r² + h²), where r is the base radius and h is the vertical height.
Why does a cube have two different surface area values (4a² and 6a²)?
4a² is the lateral (side-only) surface area of just the four vertical faces; 6a² is the total surface area including the top and bottom faces too.