Surface Area of Cylinders and Cones
Surface area is the total area of all faces (or curved surfaces) of a 3D solid. Cylinders and cones require calculating curved surfaces in addition to flat circular faces.
What You Need to Know
Key Concept Diagram
Cylinder surface area = 2 x pi x r^2 + 2 x pi x r x h (two circles plus rectangle)
Cone surface area = pi x r^2 + pi x r x l, where l is the slant height
The curved surface of a cylinder is a rectangle when unrolled
Slant height of a cone is different from perpendicular height; use Pythagoras to find it
Key Vocabulary
Surface area
The total area of all outer surfaces of a three-dimensional solid
Slant height
The distance along the sloping side of a cone from base edge to apex
Net
A 2D unfolded version of a 3D shape showing all its faces flat
Curved surface
The non-flat face of a cylinder or cone
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Find the total surface area of a cylinder with radius 3 cm and height 10 cm. (pi = 3.14)
Question 2
A cone has radius 4 cm and slant height 9 cm. What is the curved surface area? (pi = 3.14)
Question 3
A cylinder has no top or bottom (like a pipe). Which formula gives its surface area?
Key Concepts Summary
- ●Cylinder surface area = 2 x pi x r^2 + 2 x pi x r x h (two circles plus rectangle)
- ●Cone surface area = pi x r^2 + pi x r x l, where l is the slant height
- ●The curved surface of a cylinder is a rectangle when unrolled
- ●Slant height of a cone is different from perpendicular height; use Pythagoras to find it