Curved surface area
- CBSE · NCERT Class 10, Ch 12 Surface Areas and Volumes
The curved surface area of a solid is the area of its curved face only, leaving out any flat base or top.
A cylinder, a cone or a hemisphere has a curved face and one or more flat faces. The curved surface area, or CSA, counts only the curved part. The total surface area, or TSA, adds the flat faces too. For joined solids, you need the CSA of any part whose flat face is stuck to another solid, because that face is hidden.
- Cylinder: CSA = 2πrh.
- Cone: CSA = πrl, where l is the slant height.
- Hemisphere: CSA = 2πr². Its TSA, with the flat circle, is 3πr².
A small example
A cone has radius 6 cm and height 8 cm. Its slant height is √(6² + 8²) = 10 cm. So its CSA is π × 6 × 10 = 60π cm².
Where marks go
Question 34(B) of CBSE's 2026-27 Maths Standard sample paper is a wooden toy: a cone on a hemisphere. It asks for the cost of painting the hemisphere. In the 2026-27 Maths Standard marking scheme, the area is the hemisphere's CSA, 2πr² = 77 cm², for 1 mark. The cost is another 1 mark.
The flat circle is joined to the cone, so it is not painted. Using 3πr² here would change the area and the cost. The cost line then depends on the area line before it. See how step marking works.
Sources
Facts last checked against these sources on 30 September 2026.
- NCERT Mathematics, Class X, Chapter 12: Surface Areas and Volumes (reprint 2026-27) - section 12.2 · NCERT
- Mathematics Standard (041) Marking Scheme, Class X 2026-27 - Question 34(B) · CBSE Academic Unit
- Mathematics Standard (041) Sample Question Paper, Class X 2026-27 - Question 34(B) · CBSE Academic Unit
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