Volume and surface area calculator
Choose a solid, type its dimensions and this calculator returns the volume and the total surface area with the formula written out and the numbers substituted in. Cylinders, cones and spheres also show the curved surface area separately, which is the part exam questions most often ask for on its own.
Choose a solid and enter its dimensions
Volume = 502.6548 units³
Total surface area: 351.8584 units²
Curved surface area: 251.3274 units²
Volume in terms of π: 160π
Working
- V = πr²h = π × 4² × 10 = 502.6548
- Curved SA = 2πrh = 2π × 4 × 10 = 251.3274
- Total SA = 2πrh + 2πr² = 351.8584
The method behind it
- Cylinder: V = πr²h, curved SA = 2πrh, total SA = 2πrh + 2πr².
- Cone: V = ⅓πr²h, l = √(r² + h²), curved SA = πrl, total SA = πrl + πr².
- Sphere: V = (4/3)πr³, SA = 4πr². Prism: V = cross-section area × length.
How to use this tool
1. Choose the solid
Pick a cube, cuboid, cylinder, cone, sphere or triangular prism. The input boxes change to match the shape.
2. Enter the dimensions
Use the same length unit throughout. Volume comes out in cubic units and surface area in square units.
3. Check the substitution
Each step shows the formula first and then the substitution, which is where method marks are awarded.
Frequently asked questions
What is the formula for the volume of a cylinder?
Volume = πr²h, where r is the base radius and h is the height. The curved surface area is 2πrh and the total surface area adds the two circular ends: 2πrh + 2πr².
What is the surface area of a sphere?
Surface area = 4πr² and volume = (4/3)πr³. Both are given on most GCSE formula sheets, but you are expected to use them accurately.
How do you find the volume of a prism?
Volume = cross-sectional area × length. For a triangular prism the cross-section is ½ × base × height, so the volume is ½ × base × height × length.
What is slant height on a cone?
The slant height l runs from the apex to the edge of the base and satisfies l² = r² + h². Curved surface area is πrl, so you often need Pythagoras before the surface area formula.
Practise this properly, not just once
A solver gives you the answer; exam marks come from the working. MathsGradeUp pairs exam-board questions with step-by-step feedback and revision notes on the exact topics you keep dropping marks on.