Surface area formula

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:

cube-image

Surface area = 6 × a2





Right circular cylinder:

cylinder-image

Surface area = 2 × pi × r2   +  2 × pi × r × h

pi = 3.14
h is the height
r is the radius




Rectangular prism:

rectangular-solid-image

Surface area = 2 × l × w  +  2 × l × h  +  2 × w × h




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




Sphere:

Sphere-image

Surface area = 4 × pi × r2

pi = 3.14
r is the radius




Right circular cone:

Cone-image

Surface area = pi × r2  +  pi × r ×( √(h2 + r2))

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



Right square pyramid:

pyramid-image

Surface area = s2 + 2 × s × l

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



A couple of 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 cm.

The formula to use to find the surface area of cube is 6a2

6a2 = 6 × a2 =  6 × 52 = 6 × 25 = 150

The surface area of the cube is 150 cm2

Example #2.

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 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 cm2

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