Here, we provide you with a comprehensive list of surface area formula for some common three-dimensional figures such as the cube, the cylinder, the rectangular prism, the sphere, the right circular cone, and the right square pyramid.

Cube:

Surface area of a cube = 6 × a^{2}

Right circular cylinder:

Surface area of a cylinder = areas of the two bases + lateral surface area

Surface area of a cylinder = 2 × pi × r^{2} + 2 × pi × r × h

pi = 3.14
h is the height
r is the radius

Cuboid also called rectangular prism:

Surface area of a cuboid = 2lw + 2lh + 2wh = 2(lw + lh + wh)

Surface area of a rectangular prism = 2 × l × w + 2 × l × h + 2 × w × h

l is the length
w is the width
h is the height

Sphere:

Surface area of a sphere = 4 × pi × r^{2}

pi = 3.14
r is the radius

Right circular cone:

Surface area of a cone = pi × r^{2} + pi × r ×( √(h^{2} + r^{2}))

pi = 3.14
r is the radius
h is the height
l is the slant height of the cone

Right square pyramid:

Surface area of a pyramid = s^{2} + 2 × s × l

s is the length of the base
h is the height
l is the slant height

Less common surface area formulas that are important to know as well.

Hollow cylinder:

Total surface area of a hollow cylinder = 2πh(R + r) + 2π(R^{2} - r^{2})

π = 3.14
h is the height
r is the radius of the inner circle
R is the radius of the outer circle

Hemisphere:

Surface area of a hemisphere = 3πr^{2}

π = 3.14
r is the radius of the hemisphere

Examples showing how to use the surface area formula to solve some problems.

Example #1

Find the surface area of a cube if the length of one side is equal to 5 ft.

The formula to use to find the surface area of cube is 6a^{2}

6a^{2} = 6 × a^{2} = 6 × 5^{2} = 6 × 25 = 150

The surface area of the cube is 150 ft^{2}

Example #2

Find the surface area of a cylinder if the diameter of the base is 10 inches and the height of the cylinder is 8 inches.

Since the radius is half the diameter, r = 10/2 = 5

The lateral area (L.A.) is 2 × pi × r × h

L.A. = 2 × pi × r × h = 2(3.14)(5)(8)

L.A. = (6.28)(40) = 251.2

The areas of the two bases is equal to 2 × pi × r^{2}

2(3.14)(5^{2}) = 6.28(25) = 157

SA = total surface area = 251.2 + 157 = 408.5 square inches

Example #3

The dimensions of a rectangular prism are shown below

Length is equal 5 cm

Width is equal to 6 cm

Height is equal 3 cm

Find the surface area of the rectangular prism.

The formula to use to find the surface area of a rectangular prism as already shown above is 2lw + 2lh + 2wh = 2 × l × w + 2 × l × h + 2 × w × h

2 × 5 × 6 + 2 × 5 × 3 + 2 × 6 × 3

2 × 30 + 2 × 15 + 2 × 18

60 + 30 + 36

90 + 36

126

The surface area of the rectangular prism is 126 cm^{2}

Surface Area Formula FAQs

We can look for the area of a flat surface such as a rectangle or a triangle. However, we look for the surface area of a solid figure such as a cube or a cylinder.

A cube has 6 equal faces. Each face is a square. Therefore, to get the surface area, just find the area of a square and then multiply by 6.

Suppose a is the length of an edge (length of one side of a face) The formula for volume of a cube is a^{3} and the formula for surface area is 6a^{2}