Quick answer: A cylinder with radius 3 cm and height 10 cm has a surface area of 2 × π × 3 × (3 + 10) = 245.044227 cm²: 188.495559 cm² of side plus two 28.274334 cm² ends.
How it's calculated
Surface area is the total area of all the faces. A box has three pairs of rectangles, 2(lw + lh + wh); a cube has six equal squares, 6s². A cylinder has two circles and a rectangle wrapped round: 2πr² + 2πrh = 2πr(r + h).
A sphere's surface is 4πr²; a closed hemisphere adds its flat circle to the curved half, 2πr² + πr² = 3πr². A capsule is a sphere's surface plus the cylinder side: 4πr² + 2πrh.
Cones and pyramids use the slant height ℓ, measured along the side: for a cone ℓ = √(r² + h²) and the area is πr² + πrℓ; for a square pyramid ℓ = √(h² + (s/2)²) and the area is s² + 2sℓ.
Worked examples
- Cylinder r = 3, h = 10: 2π × 3 × 13 = 245.044227
- Cone r = 3, h = 4: ℓ = 5, π × 3 × (3 + 5) = 75.398224
- Cube s = 4: 6 × 16 = 96
Frequently asked questions
What is the difference between total and lateral area?
Lateral area is the sides only (for example the label on a can); total area adds the top and bottom.
How much paint do I need?
Find the area to cover, then divide by the coverage on the tin (often about 10 m² per litre per coat) and multiply by the number of coats.
How do I get the volume?
Use the volume calculator with the same dimensions.
What's the surface area of a cylinder with a 3 cm radius and 10 cm height?
About 245 cm². The two ends are 56.5 cm² together and the curved side is 188.5 cm².
How much tile does a swimming pool need?
Add the floor to the four walls and leave out the top. An 8 × 4 m pool that's 1.5 m deep has 32 m² of floor and 36 m² of wall, so 68 m², plus about 10% for cuts.
Does a box with no lid have less surface area?
Yes. Take the top, length × width, off the total.