Question 1

How do you calculate volume?

Accepted Answer

For solids with a constant cross-section (cube, cuboid, cylinder): volume = base area × height. For a cuboid that is length × width × height, for a cylinder π × r² × h. Pointed solids such as cones and pyramids have exactly one third of that volume. The sphere has its own formula: V = 4/3 × π × r³. Always convert all measurements to the same unit first.

Question 2

How do I convert cubic metres or cubic centimetres to litres?

Accepted Answer

One litre is exactly one cubic decimetre (1 l = 1 dm³). So 1 m³ = 1,000 l, 1 cm³ = 1 ml = 0.001 l and 1 mm³ = 0.000001 l. A pool of 48 m³ therefore holds 48,000 litres, a cylinder of 9,425 cm³ about 9.4 litres. The calculator shows the result in litres and all common units automatically.

Question 3

How do I calculate the volume of a cylinder?

Accepted Answer

The formula is V = π × r² × h. First calculate the circular base area π × r², then multiply by the height. If you only know the diameter, divide it by 2. Example: diameter 20 cm, height 30 cm gives r = 10 cm and V = π × 100 × 30 ≈ 9,425 cm³, about 9.4 litres.

Question 4

How do I calculate the volume of a sphere?

Accepted Answer

The volume of a sphere is V = 4/3 × π × r³. The radius is cubed: if the radius doubles, the volume becomes eight times larger. A sphere with r = 1 has a volume of about 4.18879 cubic units, a sphere with r = 10 cm about 4,189 cm³ (roughly 4.2 litres). The surface area is A = 4 × π × r².

Question 5

How do I calculate the circumference and area of a circle?

Accepted Answer

Circumference C = 2 × π × r = π × d, area A = π × r². Every other value can be derived from any single one: r = d ÷ 2, r = C ÷ (2π) or r = √(A ÷ π). In the calculator, choose "Circle" and select which value you know — radius, diameter, circumference or area.

Question 6

How does the Pythagorean theorem work?

Accepted Answer

In a right triangle, a² + b² = c². a and b are the legs at the right angle, c is the longest side, the hypotenuse. Example: a = 3 and b = 4 gives c = √(9 + 16) = 5. The angles follow from trigonometry: α = arctan(a ÷ b) ≈ 36.87° and β = 90° − α ≈ 53.13°. The calculator solves the triangle from any two known values.

Question 7

Why does a cone have only a third of a cylinder's volume?

Accepted Answer

A cone and a cylinder with the same base area and height differ in that the cone narrows evenly to its tip. Integrating the cross-sections gives exactly one third — hence V = 1/3 × π × r² × h. The same applies to a pyramid compared with a cuboid: V = 1/3 × a² × h. Put simply: three filled cones fill one cylinder.

Question 8

How much water fits in my pool?

Accepted Answer

Calculate rectangular pools as a cuboid (length × width × water depth) and round pools as a cylinder (π × r² × water depth). Use the actual fill level, not the wall height — usually 10 to 15 cm stay free. A pool of 8 × 4 m with 1.5 m water depth holds 48 m³ = 48,000 litres. Use the quick-start examples above and adjust the measurements.

Question 9

What is the difference between surface area and lateral area?

Accepted Answer

Surface area is the entire outer skin of a solid: base, top and lateral surface together. Lateral area is only the "side wall" without base and top. For a cylinder: L = 2 × π × r × h, A = 2 × π × r² + L. This matters in practice for paint, liners or insulation: a pool liner needs the floor plus the lateral area, but no top.

Guide: Volume Calculator

How to Calculate Volume: Every Formula for Cube, Cylinder, Sphere, Cone & Pyramid

Pool Volume: How Many Litres Does Your Pool Hold?

Circle Calculations: Circumference, Area, Radius and Diameter with Examples

Pythagorean Theorem: Formula, Examples and Finding Angles

Converting Litres to Cubic Metres: m³, dm³, cm³ and ml Explained

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