vmbo havo vwo
Volume calculator
Quick answer
Cube: V = a³. Sphere: V = ⁴⁄₃ π r³. Cone: V = ¹⁄₃ π r² h.
Examples: a = 4 → 64 cm³; r = 3 → 36π ≈ 113.0973 cm³; r = 3 and h = 9 → 27π ≈ 84.8230 cm³. Diameter: first r = d ÷ 2. The cylinder is a different page: V = π r² h, without ¹⁄₃.
Calculator
Choose cube, sphere, cone, cuboid, prism or pyramid — no cylinder. The cylinder is on the cylinder volume calculator. cm, m or mm is a label; we do not convert between units. The answer gets ³ after it. Numbers greater than 0.
What is volume?
Volume — Dutch school books often say inhoud — is how much fits inside. You count how many 1 cm × 1 cm × 1 cm cubes fit; that is why the unit is cm³ (or m³, mm³). Length is a line, area a plane (cm²), volume a solid (cm³) — three different quantities.
No cylinder here. The cylinder has its own page: the cylinder volume calculator with V = π r² h (without ¹⁄₃). Here you work out cube, sphere, cone, cuboid, prism and pyramid.
| Solid | Formula | Example |
|---|---|---|
| Cube | V = a³ | a = 4 cm → 64 cm³ |
| Sphere | V = ⁴⁄₃ π r³ | r = 3 cm → 36π ≈ 113.0973 cm³ |
| Cone | V = ¹⁄₃ π r² h | r = 3 cm, h = 9 cm → 27π ≈ 84.8230 cm³ |
| Cylinder (own calculator) | V = π r² h | See cylinder volume calculator |
| Conversion | Value | Watch out |
|---|---|---|
| 1 m³ in cm³ | 1,000,000 cm³ | 100 × 100 × 100 |
| 1 cm³ in mm³ | 1,000 mm³ | 10 × 10 × 10 |
| 1 m² (area) | 10,000 cm² | That is not volume |
A cube has six equal squares; every edge is a, so V = a³. A sphere is set by its radius. A cone has a circle base and a tip; its volume is one third of the cylinder with the same r and h — you work out that cylinder with the cylinder volume calculator.
Cuboid, prism and pyramid
A cuboid (Dutch: balk) has right angles everywhere: V = l × b × h. For a prism and a pyramid you use the area of the base G and the height h. Prism: V = G × h. Pyramid: V = ⅓ × G × h. If you work in cm, G is in cm². Find the base area itself with the area calculator.
Cuboid of 5 cm × 4 cm × 3 cm: 5 × 4 = 20; 20 × 3 = 60, so V = 60 cm³.
Prism with a base of 12 cm² and height 5 cm: 12 × 5 = 60, so V = 60 cm³.
Pyramid with a base of 36 cm² and height 10 cm: 36 × 10 = 360; 360 ÷ 3 = 120, so V = 120 cm³.
Examples by level
A die has edge 4 cm. What is the volume?
- FormulaV = a³
- Substitute4³ = 4 × 4 × 4
- a³64
- Unit64 cm³ (not cm²)
Three equal lengths multiplied → cube power. On vmbo (the more practical Dutch track) volume often starts with a die or a ball.
Cone with radius 3 cm and height 9 cm. What is V? Compare with the cylinder.
- FormulaV = ¹⁄₃ π r² h
- r² h3² × 9 = 9 × 9 = 81
- ¹⁄₃81 ÷ 3 = 27
- π27π ≈ 84.8230 cm³
Same r and h as a cylinder would be 81π; the cone is one third of that. Cylinder itself: cylinder volume calculator. On havo (middle Dutch track) the ¹⁄₃ and the sphere’s ⁴⁄₃ both show up.
Sphere with diameter 6 cm, plus why ⁴⁄₃ — and why is the cylinder not on this page?
- Radiusr = 6 ÷ 2 = 3 cm
- r³27
- ⁴⁄₃ r³⁴⁄₃ × 27 = 36
- Volume36π ≈ 113.0973 cm³
The ⁴⁄₃ is the school-book formula. The cylinder is a separate named intent on the cylinder volume calculator, so no multi-shape cylinder mode here. On vwo (university-preparatory track) a compound solid is the same formulas one after another — keep units the same.
Common mistakes
Wrong
Computing a cone as π r² h, without the ¹⁄₃. That is the cylinder.
Right
V = ¹⁄₃ π r² h. Open the cylinder volume calculator when you need V = π r² h.
Wrong
Putting the diameter into V = ⁴⁄₃ π r³ as if it were the radius.
Right
First r = d ÷ 2. Diameter 6 cm is radius 3 cm, then ⁴⁄₃ π r³.
Wrong
Answer in cm or cm², or “converting” 1 m³ to 10,000 cm³.
Right
Volume → cm³. 1 m³ = 100 × 100 × 100 = 1,000,000 cm³. 10,000 is 1 m².
Wrong
Expecting a cylinder mode here next to cube, sphere and cone.
Right
Cylinder: use the cylinder volume calculator. Here: cube, sphere, cone, cuboid, prism and pyramid.
Practice
vmbo Cube with edge 5 cm. What is V?
125 cm³
V = 5³ = 125 cm³.
vmbo Sphere with radius 3 cm. What is V? (4 decimal places)
113.0973 cm³
r³ = 27, ⁴⁄₃ × 27 = 36, then 36π ≈ 113.0973 cm³.
havo Cone, r = 3 cm, h = 9 cm. What is V? (4 decimal places)
84.8230 cm³
r² h = 9 × 9 = 81, 81 ÷ 3 = 27, 27π ≈ 84.8230 cm³.
havo Sphere with diameter 6 cm. Same V as for r = 3?
Yes, 113.0973 cm³
r = 6 ÷ 2 = 3 cm, then the same ⁴⁄₃ π r³.
vwo How many cm³ is 1 m³? And where do you calculate the cylinder?
1,000,000 cm³; on the cylinder volume calculator
100 × 100 × 100. Cylinder: V = π r² h on the cylinder volume calculator, not here.
vwo Why is the cone one third of the cylinder with the same r and h?
School-book formula: V_cone = ¹⁄₃ V_cylinder
Same r = 3, h = 9: cylinder π r² h = 81π, cone ÷ 3 of that = 27π. We do not re-derive the ¹⁄₃ here. Cylinder itself: cylinder volume calculator.
In class
On vmbo, volume is often a die (cube) or a ball (sphere). On havo the cone joins (the ¹⁄₃) and the sphere with ⁴⁄₃. On vwo the same formulas sit in a compound solid: first one formula, then the other, units kept equal.
Cube, sphere and cone are in this one calculator: it is always the same question (how much fits inside?). The cylinder stays on the cylinder volume calculator, because that named intent is already live. Area of a base face: area calculator.
Learning path
- Related: Cylinder volume calculator · Area calculator
Frequently asked questions
How do you calculate the volume of a cube?
V = a³. Edge 4 cm is 4 × 4 × 4 = 64 cm³.
How do you calculate the volume of a sphere?
V = ⁴⁄₃ π r³. With r = 3 cm, V = 36π ≈ 113.0973 cm³. Diameter: first r = d ÷ 2, then the same formula.
How do you calculate the volume of a cone?
V = ¹⁄₃ π r² h. r = 3 cm and h = 9 cm gives 27π ≈ 84.8230 cm³. That is one third of the cylinder with the same r and h.
Where do you calculate the volume of a cylinder?
On the cylinder volume calculator. Formula V = π r² h, without ¹⁄₃. This page has no cylinder mode.
How many cm³ is 1 m³?
1 m³ = 1,000,000 cm³ (100 × 100 × 100). Do not confuse that with 1 m² = 10,000 cm².