Formulas for the surface area of figures

The area of a geometric figure is a numerical characteristic of a geometric figure showing the size of the figure (part of the surface bounded by the closed contour of the figure). The area is expressed as the number of square units it contains.

surface area of a cube
surface area of a rectangular parallelepiped
surface area of a cylinder
surface area of a cone
surface area of a sphere

Surface area of a cube

Surface area of a cube via edge length

The surface area of a cube equals the square of the length of its edge multiplied by six.

S = 6 \cdot a^{2}

where S is the surface area of the cube,
a is the length of the edge of the cube.

Surface area of a cube via face diagonal

The surface area of a cube equals the ratio of six times the length of the face diagonal of the cube to the square root of two.

S = \frac{6 \cdot d}{\sqrt{2}}

where S is the surface area of the cube,
d is the length of the diagonal of the cube.

Surface area of a rectangular parallelepiped

The surface area of a rectangular parallelepiped equals the sum of the areas of all its sides.

S = 2 \cdot (a \cdot b + a \cdot h + b \cdot h)

where S is the surface area of the rectangular parallelepiped,
a is the length,
b is the width,
h is the height.

Surface area of a cylinder

The lateral surface area of a circular cylinder equals the product of the perimeter of its base and the height.

S = 2 \cdot π \cdot R \cdot h

The total surface area of a circular cylinder equals the sum of the lateral surface area of the cylinder and twice the area of the base.

S = 2 \cdot π \cdot R \cdot h + 2 \cdot π \cdot R^{2} = 2 \cdot π \cdot R \cdot (R + h)

where S is the surface area of the cylinder,
R is the radius of the cylinder,
h is the height of the cylinder.

Surface area of a cone

The lateral surface area of a cone equals the product of its radius and its slant height, multiplied by pi.

S = π \cdot R \cdot l

The total surface area of a cone equals the sum of the area of the base of the cone and the lateral surface area.

S = π \cdot R^{2} + π \cdot R \cdot l = π \cdot R \cdot (R + l)

where S is the surface area of the cone,
R is the radius of the base of the cone,
l is the slant height of the cone.

Surface area of a sphere

The surface area of a sphere equals four times its radius squared multiplied by pi.

S = 4 \cdot π \cdot R^{2}

The surface area of a sphere equals the square of its diameter multiplied by pi.

S = π \cdot D^{2}

where S is the surface area of the sphere,
R is the radius of the sphere,
D is the diameter of the sphere.

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