A cylinder's curved surface unrolls into a rectangle, so its area is 2πrh. Add the two circular ends, 2πr², for the total surface area.
A cone's curved surface area is πrl, where l is the slant height. A sphere's surface area is 4πr². If you are given the vertical height of a cone, find the slant height with Pythagoras first: l² = r² + h². A hemisphere's total surface area is 2πr² for the curve plus πr² for the flat circle.
Worked example
A sphere has radius 8 cm. Find its surface area to 1 d.p.
- Surface area = 4πr² = 4 × π × 64.
- 256π = 804.24…
Answer:804.2 cm²
Key words
- curved surface area
- the area of the curved part only
- slant height
- the sloping length of a cone
- hemisphere
- half a sphere
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Common Core-referenced: HSG-GMD.A.3