The total area of all the faces or surfaces that enclose a three-dimensional object, measured in square units.
How much wrapping paper would you need to completely cover every face of a gift box?
Showing a random 20 of 50 problems.
Example 1
medium
A cube has surface area 96. What is its volume?
Example 2
hard
A cylinder is inscribed in a cube of edge 6 (so it just fits, tangent to all four side faces). Find the lateral surface area of the cylinder in terms of π.
Example 3
medium
A cube of side 4 is painted, then cut into unit cubes. Two opposite faces' worth of painted area — what is the total painted surface area of the original cube?
Example 4
easy
Find the total surface area of a square pyramid with base side 4 and slant height 6.
Example 5
easy
Find the surface area of a cube with side 2 cm.Cube with side length 2 cm
Example 6
medium
Find the surface area of a cylinder with radius 4 cm and height 7 cm. Leave your answer in terms of π.Cylinder with r = 4 cm and h = 7 cm
Example 7
easy
Find the surface area of a rectangular box with length 5, width 4, height 2.Rectangular box with l
Example 8
medium
A closed cylinder has radius 2 cm and height 10 cm. Find its surface area in terms of π.Closed cylinder with r
Example 9
easy
Two cubes have edge lengths 2 and 5. What is the ratio of their surface areas?
Example 10
medium
Find the surface area of a cylinder with radius 3 and height 5 (in terms of π).Cylinder with r
Example 11
challenge
Why does a small animal lose body heat faster than a large one, in terms of surface-area-to-volume ratio?
Example 12
easy
Find the surface area of a cube with side 1.
Example 13
hard
A cylinder has the same surface area as a cube with edge 6. If the cylinder has radius 3, find its height in terms of π.
Example 14
medium
A cube has surface area 150 cm². Find the length of one edge.
Example 15
medium
Find the surface area of a cube whose space diagonal is 75.
Example 16
medium
A hemisphere has radius 4. Find its total surface area (curved surface + flat disk) in terms of π.
Example 17
medium
Find the surface area of a sphere with radius 3 (in terms of π).Sphere with r
Example 18
easy
Which uses square units: the amount of paint to cover a ball, or the air inside it?
Example 19
challenge
A cube and a sphere both have surface area S. Show which encloses more volume, and name the principle.
Example 20
easy
Find the surface area of a rectangular prism with length 4 cm, width 3 cm, and height 5 cm.Rectangular prism with l = 4 cm, w = 3 cm, h = 5 cm