Surface Area Formulas (video lessons, examples, step-by-step solutions) (2024)

Table of Contents

Surface Area Of A Cube Rectangular Solid Or Cuboids Surface Area Of Prism Surface Area Of Sphere Surface Area Of Solid Cylinder Surface Area Of Hollow Cylinder Surface Area Of Cone Surface Area Of Pyramid FAQs

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 s².Since a cube has six square-shape sides, its total surface area is 6 times s².
Surface area of a cube = 6s²

Worksheets and More Examples:
,
More examples on the Volume of Cubes,
More examples on the Surface Area of Cubes

How to find the surface area of a cube using the formula?
Total surface area = 6s² 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 = 2lw

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

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

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

Worksheets and More Examples on Rectangular Prisms:
,
More examples on the Volume of Cuboids,
More examples on the Surface Area of Cuboids

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 calledlateral 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:
,
More examples on the Volume of Prisms,
More examples on the Surface Area of Prisms

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 theradius.

Surface area of a sphere with radius r = 4 πr²

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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See Also
6.5: Area, Surface Area and Volume Formulas

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 = 2πr² + 2πrh = 2πr (r + h)

Worksheets and More Examples:
Worksheets: Volume of Cylinders,
Worksheets: Surface Area of Cylinders,
,
,
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

= 2πrh + 2πRh + 2(πR² − πr²)

Surface Area Of Cone

A cone is a solid with a circular base. It has acurved surface which tapers (i.e. decreases in size) to avertex at the top. Theheight 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
= πrs + πr²= πr(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 triangularlateral faces. The lateral faces meet at a commonvertex. 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 = b² + 2bs
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,
,
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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Surface Area Formulas (video lessons, examples, step-by-step solutions) (2024)

FAQs

How to do surface area step by step? ›

Multiply the length and width, or c and b to find their area. Multiply this measurement by two to account for both sides. Add the three separate measurements together. Because surface area is the total area of all of the faces of an object, the final step is to add all of the individually calculated areas together.

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How to find surface area 6th grade? ›

To calculate surface area, we add the areas of all the faces of the three-dimensional figure.

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How do you teach surface area to kids? ›

To measure surface area, which is a measurement of all the space that the surface of a three-dimensional shape takes up, we need to remember to think about covering a box. Determine how many sides there are, then find the area of each side. Add the areas of all the sides together, and you have your surface area!

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How do you write surface area answer? ›

Surface Area Formulas:

Volume = (1/3)πr²h.
Lateral Surface Area = πrs = πr√(r² + h²)
Base Surface Area = πr²
Total Surface Area. = L + B = πrs + πr² = πr(s + r) = πr(r + √(r² + h²))

Oct 4, 2023

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What is the simple formula for surface area? ›

Variables:

Surface Area Formula	Surface Area Meaning
SA=2B+Ph	Find the area of each face. Add up all areas.
SA=B+12sP	Find the area of each face. Add up all areas.
SA=2B+2πrh	Find the area of the base, times 2, then add the areas to the areas of the rectangle, which is the circumference times the height.

2 more rows

Sep 17, 2020

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What is an example of a surface area? ›

The surface area of a polyhedron is the number of square units that covers all the faces of the polyhedron, without any gaps or overlaps. For example, if the faces of a cube each have an area of 9 cm², then the surface area of the cube is 6⋅9, or 54 cm².

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How to calculate total surface area? ›

Finding the total surface area of an object means finding the surface area of each of the object's individual faces and then adding the measurements together. For instance, a cube is made of six squares. To find the total surface area of a cube, first find the area of one face of the cube and then multiply it by six.

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How do you solve surface area questions? ›

Surface Area and Volume Formulas:

Total surface area of a cuboid = 2[lb + bh + lh]
Total surface area of a cube = 6(side) ...
Lateral surface area of a cuboid = Area of walls of a room = 2(l + b) × h.
Lateral surface area of a cube = 4a. ...
Curved surface area of cylinder = 2πrh.
Total surface area of a cylinder = 2πr(r + h)

More items...

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How do you teach area in a fun way? ›

Classroom Activities for Teaching About Area

Graphitti. Give students a sheet of graph paper and have them draw shapes. ...
Area Bingo. Play a modified game of Bingo with your students. ...
Paper Shapes. Cut up paper shapes and find the area of each. ...
Ten Square Units.

What is surface area in easy words? ›

Surface area measures the space needed to cover the outside of a three-dimensional shape. Surface area is the sum of the areas of the individual sides of a solid shape. Surface area is measured in square units. There are formulas to find the surface area of different solid shapes.

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How to introduce area lesson plan? ›

Start the class by asking students if they have heard of the words "area" and "perimeter". Define these terms and give a few examples (e.g. the area of a room, the perimeter of a fence). Show different shapes on the board and ask students to define what the area and perimeter of those shapes are.

What are the key words for surface area? ›

Some keywords that pertain to surface area are cover, surface, or square units. Volume: The volume of a three-dimensional object is the amount of space that the object takes up, or the amount of space it takes to fill an object. Some keywords you may encounter that pertain to volume are fill, capacity, or cubic units.

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What is the formula for calculating area? ›

The basic formula for calculating area is Length times Width (LxW). If you are estimating the area for a rectangle you'll always use LxW. If you are calculating the area for a square you can multiply the length of one Side times itself, or (S²). The illustration above shows a room 12′ wide by 20′ long.

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How do you find area step by step? ›

The simplest (and most commonly used) area calculations are for squares and rectangles. To find the area of a rectangle, multiply its height by its width. For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area.

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Why do you calculate surface area? ›

The surface area of a three-dimensional object is the total area of all its faces. In real-life we use the concept of surface areas of different objects when we want to wrap something, paint something, and eventually while building things to get the best possible design.