Surface area formula
Here, we provide you with a comprehensive list of surface area formula for some common threedimensional figures such as the cube, the cylinder, the rectangular prism, the sphere, the right circular cone, and the right square pyramid.
Cube:
Surface area = 6 × a
^{2}
Right circular cylinder:
Surface area = 2 × pi × r
^{2} + 2 × pi × r × h
pi = 3.14
h is the height
r is the radius
Rectangular prism:
Surface area = 2 × l × w + 2 × l × h + 2 × w × h
l is the length
w is the width
h is the height
Sphere:
Surface area = 4 × pi × r
^{2}
pi = 3.14
r is the radius
Right circular cone:
Surface area = 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
Right square pyramid:
Surface area = s
^{2} + 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 6a^{2}
6a^{2} = 6 × a^{2} = 6 × 5^{2} = 6 × 25 = 150
The surface area of the cube is 150 cm^{2}
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 cm^{2}

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