**Related Pages**

Surface Area of Cuboids

Surface Area of Prisms

Surface Area of a Sphere

More Geometry Lessons

The following table gives the surface area formulas for solid shapes or three-dimensional shapes.Scroll down the page if you need more explanations about the formulas, how to use them as well asworksheets.

### Surface Area Of A Cube

A cube is a three-dimensional figure with six equal square sides. The figure below shows a cube with sides s.

If *s* is the length of one of its sides, then the area of each side of a cube is *s*^{2}.Since a cube has six square-shape sides, its total surface area is 6 times *s*^{2}.

Surface area of a cube = 6*s*^{2}

**Worksheets and More Examples:**

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More examples on the Volume of Cubes,

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**How to find the surface area of a cube using the formula?**

Total surface area = 6*s*^{2} where *s* is the length of a side.

**Example:**

Given a side of 3 cm, find the surface area of the cube.

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### Rectangular Solid Or Cuboids

A rectangular solid is also called a rectangular prism or a cuboid. In a rectangular solid,the length, width and height may be of different lengths.

The surface area of the above cuboid would be the sum of the area of all the surfaces which arerectangles.

Total area of top and bottom surfaces is *lw* + *lw = *2*lw*

Total area of front and back surfaces is *lh* + *lh = *2*lh*

Total area of the two side surfaces is *wh* + *wh = *2*wh*

Surface area of rectangular solid = 2*lw* + 2*lh* +2*wh* = 2(*lw* + *lh* + *wh*)

**Worksheets and More Examples on Rectangular Prisms:**

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More examples on the Volume of Cuboids,

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**How to find the surface area of a rectangular prism or cuboid?**

**Example:**

Find the surface of a rectangular prism with sides 18ft, 15ft and 20ft.

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### Surface Area Of Prism

A **prism** is a solid that has two parallel faces which arecongruent polygons at both ends. These faces form the **bases** ofthe prism. The other faces are in the shape of rectangles. They are called**lateral faces**. A prism is named after the shape of its base.

The surface area of a prism is the sum of the area of all its external faces.

We can also use the formula:

Surface area of prism = 2 × area of base + perimeter of base × height

**Worksheets and More Examples:**

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More examples on the Volume of Prisms,

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**How to find the surface area of a triangular prism by adding the area of the external faces?**

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**How to find the surface area of a triangular prism using the formula SA = ab+(s1+s2+s3)h?**

where

a = altitude (height of the triangular face)

b = base of triangle

h = height of prism or distance between the two triangular faces.

s1, s2 and s3 are the three sides of the triangle

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### Surface Area Of Sphere

A **sphere** is a solid in which all the points on the roundsurface are equidistant from a **fixed point**, known asthe center of the sphere. The distance from the center to the surface is the**radius**.

Surface area of a sphere with radius *r* = 4 π*r*^{2}

**Worksheets and More Examples:**

Worksheets: Volume of Spheres,

Worksheets: Surface Area of Spheres,

More examples on the Volume of Spheres,

More examples on the Surface Area of Spheres

**How to find the surface area of a sphere?**

**Example:**

Find the surface area of a sphere with r = 4ft. (leave answer in terms of π)

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### Surface Area Of Solid Cylinder

A cylinder is a solid that has two parallel faces which are **congruent circles**. These facesform the **bases** of the cylinder. The cylinder has one **curved surface**.

The **height** of the cylinder is the perpendicular distance between the two bases.

The net of a solid **cylinder** consists of 2 circles and one rectangle. The curved surfaceopens up to form a rectangle.

Surface area = 2 × area of circle + area of rectangle

Surface Area = 2π*r*^{2} + 2π*rh* = 2π*r *(*r + h*)

**Worksheets and More Examples:**

Worksheets: Volume of Cylinders,

Worksheets: Surface Area of Cylinders,

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More examples on the Volume of Cylinders,

More examples on the Surface Area of Cylinders

**How to find the surface area of a cylinder?**

How to obtain the total surface of a cylinder by looking at the net of the cylinder?

**Example:**

Find the surface area of a cylinder with radius 5 and height 12.

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### Surface Area Of Hollow Cylinder

Sometimes you may be required to calculate the total surface area of a hollow cylinder or tube.

Total surface area of hollow cylinder

= area of internal curved surface + area of external curved surface + area of the two rings

= 2π*rh* + 2π*Rh +* 2(*πR*^{2} − πr^{2})

### Surface Area Of Cone

A cone is a solid with a circular **base**. It has a**curved surface** which tapers (i.e. decreases in size) to a**vertex** at the top. The**height** of the cone is the perpendicular distance from thebase to the vertex.

The net of a solid **cone** consists of a small circle and a sector of a largercircle. The arc of the sector has the same length as the circumference of the smaller circle.

Surface area of cone = Area of sector + area of circle

= π*rs* + π*r*^{2}= π*r*(*r* + *s*)

**Worksheets and More Examples:**

Worksheets: Volume of Cones,

More examples on the Volume of Cones,

More examples on the Surface Area of Cones

**How to find the surface area of a cone?**

**Example:**

Find the surface area of a cone with radius = 9cm, vertical height = 12cm and slant height = 15cm. (Leave answer in π form)

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### Surface Area Of Pyramid

A pyramid is a solid with a polygonal **base** and several triangular**lateral faces**. The lateral faces meet at a common**vertex**. The **height** of the pyramid is the perpendiculardistance from the base to the vertex.

A pyramid is named after the shape of its base. A rectangular pyramidhas a rectangle base. A triangular pyramid has a triangle base.

We can find the surface area of any pyramid by adding up the areas of its lateral faces and its base.

Surface area of any pyramid = area of base + area of each of the lateral faces

If the pyramid is a regular pyramid, we can use the formula for the surface area of a regular pyramid.

Surface area of regular pyramid = area of base + 1/2 *ps*

where *p* is the perimeter of the base and *s* is the slant height.

If the pyramid is a square pyramid, we can use the formula for the surface area of a square pyramid.

Surface area of square pyramid = *b*^{2} + 2*bs*

where *b* is the length of the base and *s* is the slant height.

**Worksheets and More Examples on Rectangular Prisms:**

Worksheets: Volume of Square Pyramids,

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More examples on the Volume of Pyramids,

More examples on the Surface Area of Pyramids

**How to find the surface area of regular pyramid?**

**Example:**

Find the surface area of a regular pyramid with side = 40in, height = 39in and slant height = 44in.

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