How to calculate the volume of 3D shapes (examples and jobs using modelling skills)
The ability to apply geometric concepts, such as calculating volume, can be beneficial in many professional careers. Calculating volume is a metric used for three-dimensional (3D) modelling that applies to fields like design, drafting and engineering. To learn to calculate volume, there are precise formulas based on the shape of the object you're measuring. In this article, we explain what the volume of a 3D object is, how to calculate the volume of different shapes with helpful examples and what jobs often rely on 3D modelling skills.
What is volume?
To know how to calculate volume, it's crucial to first understand what volume is. Volume is the 3D space occupied by a figure or object. Finding the volume can help to determine the amount required to fill an object, like a bottle of water or a canister. As measuring 3D shapes requires three degrees of measurement, it's necessary to record volume in cubic units, including both metric and imperial cubic units.
For instance, if you calculate the volume of a shape in centimetres, indicate the result in cubic centimetres. Volume applies to both solid and liquid capacities, such as cubic centimetres, metres, millilitres and litres.
How to calculate the volume of a 3D figure
Understanding how to calculate volume can help when reviewing common 3D shapes:
1. Calculate the volume of a cube
By definition, a cube is a three-dimensional box shape with equal side lengths. The formula for volume is:
V = s³ or the length x width x height
For example, if the side length of a cube is 5 centimetres, the calculation for volume is 5 x 5 x 5 = 125 cubic centimetres.
2. Calculate the volume of a cylinder
A cylinder is a 3D figure that has two identical circular flat ends, such as a can, so to calculate the volume of a cylinder, it's necessary to use pi (π) and to know the radius of the circle. The formula is:
V = πr²h or 3.14 x the radius raised to the second power x the height
The volume of a cylinder with a radius of 5 millimetres and a height of 8 millimetres is 3.14 x 25 x 8 = 628 cubic millimetres.
3. Calculate the volume of a rectangular prism
A rectangular prism is a box-shaped figure, for instance, a shoebox. To calculate the volume, it's necessary to use this formula:
length x width x height of the prism or V = lwh
For example, if a rectangular shape is 16 centimetres long, 8 centimetres wide and 10 centimetres high, the calculation for the volume is 16 x 8 x 10 = 1,280 cubic centimetres.
4. Calculate the volume of a regular pyramid
A regular pyramid has a square base with four equilateral triangular sides and the formula for calculating the volume is:
V = 1/3bh, meaning 1/3 of the base x the height
To begin, remember to calculate the area of the base (A = s²), so a pyramid with a side length of 2 metres has a base area that equals 4 square meters. If the height is 3 metres, the volume of the pyramid is .33 x 4 x 3 = 3.96 cubic metres.
5. Calculate the volume of a cone
A cone is a circular pyramid consisting of a circular base with a cylinder shape tapering to a point. As the base is a circle, using pi is necessary for calculating the volume and the formula is:
V = 1/3πr²h
For instance, calculating the volume of a cone with a radius of 3 centimetres and a height of 12 centimetres is .33 x 3.14 x 9 x 12 = 111.91 cubic centimetres.
6. Calculate the volume of a sphere
A sphere is a perfectly round shape, like a ball, that also requires pi to measure volume. The formula for calculating is:
V = 4/3πr³, with the radius raised to the power of three
For example, if you're calculating the volume of a spherical figure and the radius is 6 millimetres, multiply 1.33 x 3.14 x 216 = 902.06 cubic millimetres.
Examples of calculating volume
To better understand how calculating volume can be helpful in different situations, here are two examples of applications:
A pet store owner sells fish aquariums at their shop and wants to ensure that customers understand the correct amount of water to use when filling their aquariums. For an aquarium that measures 80 centimetres long, 35 centimetres wide and 40 centimetres high, the store owner uses the formula for calculating volume for a rectangular prism, V = lwh.
This yields a volume of 80 x 35 x 40 = 112,000 cubic centimetres. Although this volume only measures the inner space of the aquarium, the pet store owner can use it to estimate how many litres of water are necessary to fill the aquarium based on the volume.
A visual artist who casts epoxy and resin art projects has acquired a cylinder mould for creating some of their pieces. To determine how much space is available in the mould, the artist uses the formula for measuring the volume of a cylinder, which is V = πr²h. If the radius is 6 centimetres and the height is 25 centimetres, the calculation is 3.14 x 36 x 25 = 2,826 cubic centimetres.
Difference between volume vs area
When performing mathematical calculations, volume differs from the area. Volume measures the space occupied by a 3D shape and area measures the surface region of a shape or object. Unlike volume, which calculates in cubic units, you multiply area in square units. For example, when measuring the area of a room, you multiply the length of the room by the width, such as 6 metres x 4 metres = 24 square metres. To measure the cubic volume of the room, you calculate the length x width x height.
Jobs that use 3D modelling skills
Here are professions that commonly use 3D modelling skills:
A maths teacher at the secondary level most often works with adolescent and young adult students. They can teach a range of mathematical subjects, including geometry, algebra and trigonometry. At the secondary level, maths teachers educate their students about calculating volume and 3D space as part of their geometry lessons.
An architect designs building plans and blueprints for homes, offices and buildings. They most often work with clients to develop plans based on their clients' needs and preferences. Creating a schematic design for a home, office or building usually involves drawings and 3D renderings.
An animator works in the arts and entertainment industry and creates stories through moving images. Some of their tasks include developing storyboards, drafting designs and using specialised technical software to finalise their images for use. Understanding and calculating shapes and sizes, including 3D figures, are important aspects of an animator's job.
An interior designer creates designs for residential or business settings. Key aspects of their job include meeting with their clients and developing plans for their living or workspaces. As part of their professional role, it's typically necessary for an interior to create 3D renderings of their proposed designs for their clients.
A fashion designer works in the fashion industry and creates designs for clothing, shoes and accessories. After finalising their designs, fashion designers commonly oversee the production of their work. To help envision their design creations on a model, many fashion designers rely on 3D modelling.
A packaging engineer is most often responsible for developing product packaging solutions for a business. They're knowledgeable about both graphic and package design. To be successful at their jobs, packaging engineers are competent in 3D modelling and simulation for developing package designs.
Computer-aided design (CAD) specialist
A CAD specialist is someone who uses CAD software to create technical drawings, such as plans for cars, bridges or buildings. They often work with architects or construction professionals to develop the designs. A CAD specialist's primary responsibility is typically to create 3D images for construction projects.
A robotics engineer designs and develops robotics systems to improve the efficiencies of various industries, including healthcare, manufacturing and agriculture. They're responsible for creating robots or robotic systems that perform different tasks and functions. Given their job duties, it's important for robotics engineers to be knowledgeable about 3D modelling.
A game designer creates video games for computers, consoles or mobile devices. They're responsible for generating design concepts and planning for the various elements of video games. Having an understanding of 3D objects and shapes is usually required to work as a game designer.