vmbo havo vwo
Cylinder volume calculator
Quick answer
Volume (Dutch school books often say inhoud): V = π r² h. Radius 3 cm, height 10 cm: V = π · 9 · 10 ≈ 282.7433 cm³.
If you have the diameter: r = d ÷ 2. The unit on the answer is the same as r and h, to the third power.
Calculator
Cylinder only. Choose radius or diameter; enter the height. cm, m or mm is a label; we do not convert between units. No cube, sphere or cone here — those are on the volume calculator.
What is the volume of a cylinder?
A cylinder has two equal circles and a straight height between them. The volume — in Dutch school wording inhoud, meaning volume or capacity — is the base-circle area times the height: first π r², then × h. That is how much fits inside, in cm³ (or m³, mm³).
| Idea | Formula | Example |
|---|---|---|
| Cylinder volume | V = π r² h | r = 3 cm, h = 10 cm → 90π ≈ 282.7433 cm³ |
| Radius from diameter | r = d ÷ 2 | d = 6 cm → r = 3 cm |
| Base circle (step) | A = π r² | r = 3 → 9π cm², then × h |
On vmbo (the more practical Dutch track) you practice this with cans and pipes. On havo and vwo (middle and university-preparatory tracks) the same V = π r² h returns in compound solids. Cube, sphere and cone: volume calculator — no second cylinder mode there. Missing a length in a right cross-section: Pythagorean theorem calculator.
Examples by level
r = 3 cm, h = 10 cm. What is V?
- r²3² = 9
- π r²9π (base circle in cm²)
- π r² h9π × 10 = 90π ≈ 282.7433 cm³
First the circle area, then × height for volume.
Diameter 6 cm, height 10 cm. Same cylinder as r = 3?
- Radiusr = d ÷ 2: 6 ÷ 2 = 3 cm
- FormulaV = π · 3² · 10 = 90π
- Answer≈ 282.7433 cm³ — the same V
Putting the diameter straight into V = π d² h doubles the radius in the square by mistake.
Why must r and h use the same unit? And how does a cone compare to this cylinder?
- Dimensionr² h has unit length³ → cm³
- Mix3 cm and 0.1 m mixed gives a wrong answer; convert everything to cm or everything to m first
- ConeWith the same r and h, V_cone = ⅓ V_cylinder. That formula is on the volume calculator, not here.
This tool does not convert units and has no multi-shape mode.
Common mistakes
Wrong
V = π d² h: squaring the diameter as if it were the radius.
Right
First r = d ÷ 2, then r². Or V = π (d/2)² h. d = 6 → r = 3.
Wrong
Writing only π r² and calling it volume (that is still cm²).
Right
π r² is the base circle. Volume: still × h → cm³.
Wrong
Using the cone formula ⅓ π r² h for a cylinder, or the other way around.
Right
Cylinder: V = π r² h, without ⅓. Cone: volume calculator.
Wrong
r = 0 or h = 0, or cm and m in one sum without converting.
Right
Radius and height greater than 0, same unit. This tool does not convert.
Practice
vmbo r = 2 cm, h = 5 cm. What is V in terms of π?
20π cm³
π × 2² × 5 = 4π × 5 = 20π cm³.
vmbo r = 3 cm, h = 10 cm. What is V? (4 decimal places)
282.7433 cm³
90π ≈ 282.7433 cm³.
havo d = 4 cm, h = 3 cm. What is r, and what is V in terms of π?
r = 2 cm, V = 12π cm³
Diameter ÷ 2 gives r = 2. Then V = π × 2² × 3 = 12π cm³.
havo Diameter 6 cm, h = 10 cm. Same V as for r = 3 cm?
Yes, ≈ 282.7433 cm³
r = 6 ÷ 2 = 3 cm, then the same 90π.
vwo Can you mix 3 cm and 10 m in one calculation?
No without converting. First the same unit (for example 3 cm and 1000 cm).
vwo r = 3 cm, h = 9 cm. What is V of the cylinder, and what would the cone with the same r and h be?
Cylinder 81π cm³; cone 27π cm³
Cylinder: π · 9 · 9 = 81π. Cone = ⅓ of that = 27π — on the volume calculator.
In class
Solid volumes sit in the Dutch math exam programs. On vmbo the cylinder is often a can or a pipe: V = π r² h with cm³. On havo/vwo the same formula appears in a compound solid, or next to the cone (⅓ of this volume for equal r and h).
Cube, sphere and cone are on the volume calculator — without a cylinder mode, so this named intent stays here. The base circle π r² is also practiced on the area calculator. Lateral surface area is 2π r h; that is a different formula, later on its own page.
Learning path
- Related: Volume calculator · Area calculator
Frequently asked questions
How do you calculate the volume of a cylinder?
V = π r² h. First the base circle π r², then × height. r = 3 cm, h = 10 cm → 90π ≈ 282.7433 cm³.
What if you have the diameter?
r = d ÷ 2, then the same formula V = π r² h. Diameter 6 cm is radius 3 cm. Do not put d straight into r².
Why cm³ and not cm²?
Volume is length × length × length. π r² is still area (cm²); times h gives cm³. Circle area is on the area calculator.
Where do you calculate cube, sphere or cone?
On the volume calculator. That page has no cylinder mode; the cylinder stays here with V = π r² h.
Can you mix radius in cm and height in m?
Not without converting first. Put everything in cm or everything in m. This tool does not convert between units.
Related tools
Volume calculator
Cube, sphere and cone. No second cylinder page — the cylinder stays here.
Pythagorean theorem calculator
When you need a missing length in a right cross-section.
Area calculator
Base circle π r², plus rectangle and triangle — plane, not volume.
Geometry
Overview of the geometry tools: the cylinder, and cube, sphere and cone.