Surface Area of 3D Shapes
Surface area is the total area of all outer faces of a solid. Calculating it requires identifying each face, finding its area, and adding them together.
What You Need to Know
Key Concept Diagram
Surface area of a rectangular prism = 2(lb + lh + bh) where l, b, h are length, breadth, height
Surface area of a cylinder = 2πr² + 2πrh (two circles plus curved surface)
Surface area of a cone = πr² + πrl where l is slant height
Surface area of a sphere = 4πr²
Key Vocabulary
Surface area
The total area of all the outer surfaces of a three-dimensional shape
Net
A flat pattern that can be folded to form a 3D shape; useful for finding surface area
Slant height
The distance along the sloping surface of a cone from base edge to apex
Lateral surface
The curved or sloped surfaces of a solid, excluding the base(s)
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
A cube has side length 4 cm. What is its total surface area?
Question 2
Which formula gives the curved surface area of a cylinder with radius r and height h?
Question 3
The total surface area of a sphere with radius 6 cm is:
Key Concepts Summary
- ●Surface area of a rectangular prism = 2(lb + lh + bh) where l, b, h are length, breadth, height
- ●Surface area of a cylinder = 2πr² + 2πrh (two circles plus curved surface)
- ●Surface area of a cone = πr² + πrl where l is slant height
- ●Surface area of a sphere = 4πr²