vmbo havo vwo
Geometry
What belongs here
Geometry is length, plane and solid. Four tools: Pythagorean theorem, area (rectangle, triangle, circle), cylinder volume, and volume (cube, sphere, cone). On the Dutch site this topic is called Meetkunde (geometry).
In which order do you build this?
- Pythagoras: missing side in a right triangle
- Area: how large is the plane
- Cylinder: circle area times height
- Other solids: cube, sphere and cone
Start with the Pythagorean theorem calculator when a length is missing (a² + b² = c²). Go to the area calculator for cm²: l × b, ½bh, π r². The cylinder volume calculator reuses that circle: V = π r² h. Other solids on the volume calculator: a³, ⁴⁄₃ π r³, ¹⁄₃ π r² h — without a cylinder mode. Unit: cm, cm², cm³ — do not mix them.
Which tool do you pick?
| You see in the sum… | Open |
|---|---|
| Right triangle, missing side | Pythagorean theorem calculator |
| Plane: floor, tile, circle (cm²) | Area calculator |
| Can, pipe, cylinder (V = π r² h) | Cylinder volume calculator |
| Cube, sphere or cone (cm³) | Volume calculator |
Unsure between area and volume: cm² is plane, cm³ is solid. Unsure between cylinder and volume: for a cylinder, use the cylinder volume calculator.
What you meet per level
On this hub: which geometry tool fits which kind of sum. The current exam program is on Examenblad. Dutch secondary tracks are named once: vmbo, havo and vwo.
On vmbo, geometry is often a ladder against a wall (Pythagoras with a 3-4-5 triangle), a floor or tile (area in cm²), a can or pipe (cylinder), and a die or ball (cube, sphere). Fill formulas with the same unit; do not swap radius and diameter.
On havo you chain steps: first a missing side with Pythagoras, then the triangle area; or diameter → radius → π r² → times height for the cylinder. The cone is one third of that (¹⁄₃ π r² h) on volume. Compound figures are the same formulas one after another, not a new law.
On vwo the same tools inside a larger figure: a right cross-section in a cylinder, or a sphere plus cone as a compound solid. No extra theorems on this hub. Degrees as their own tool come later; until then the Dutch scientific calculator covers sin/cos/tan.
Tools
Pythagorean theorem calculator
Hypotenuse or a leg when one length is missing in a right triangle. Open this first for length.
vmbo havo vwoArea calculator
How large is the plane: rectangle, triangle, circle — answer stays in cm².
vmbo havo vwoCylinder volume calculator
Can or pipe: base circle times height. Its own calculator, separate from the volume calculator.
vmbo havo vwoVolume calculator
How much fits inside a cube, sphere or cone — cylinder lives on its own page.
Topics by level
- vmbo, havo and vwo: Pythagorean theorem calculator · Area calculator · Volume calculator · Cylinder volume calculator · SOHCAHTOA calculator
- Explore: Pythagoras simulation · SOHCAHTOA simulation
- Math A or math B in havo or vwo? Difference between math A and B