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Jul 30, 2024 · Volume is the amount of space that an object or substance occupies. Generally, the volume of a container is understood as its capacity — not the amount of space the container itself displaces. Cubic meter (m 3) is an SI unit for volume. However, the term volume may also refer to many other things, such as.
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What is Volume? Every three-dimensional object occupies some space. This space is measured in terms of its volume. Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.
- Overview
- Calculating the Volume of a Cube
- Calculating the Volume of a Rectangular Prism
- Calculating the Volume of a Cylinder
- Calculating the Volume of a Regular Square Pyramid
- Calculating the Volume of a Cone
- Calculating the Volume of a Sphere
- Worksheet and Practice Problems
The volume of a shape is the measure of how much three-dimensional space that shape takes up.
You can also think of the volume of a shape as how much water (or air, or sand, etc.) the shape could hold if it was filled completely. Common units of volume include cubic centimeters (cm
), and cubic feet (ft
This article will teach you how to calculate the volume of six different three-dimensional shapes that are commonly found on math tests, including cubes, spheres, and cones. You might notice that a lot of the volume formulas share similarities that can make them easier to remember. See if you can spot them along the way!
A cube is a three-dimensional shape that has six identical square faces.
In other words, it is a box shape with equal sides all around.
A 6-sided die is a good example of a cube you might find in your house. Sugar cubes, and children's letter blocks are also usually cubes.
Learn the formula for the volume of a cube.
Since all of the side lengths of a cube are the same, the formula for the volume of a cube is really easy. It is V = s
where V stands for volume, and s is the length of the sides of the cube.
A rectangular solid, also known as a rectangular prism, is a three-dimensional shape with six sides that are all rectangles.
In other words, a rectangular solid is simply a three-dimensional rectangle, or box shape.
A cube is really just a special rectangular solid in which the sides of all of the rectangles are equal.
Learn the formula for calculating the volume of a rectangular solid.
The formula for the volume of a rectangular solid is Volume = length * width * height, or V = lwh.
Find the length of the rectangular solid.
Learn to identify a cylinder.
A cylinder is a three-dimensional shape that has two identical flat ends that are circular in shape, and a single curved side that connects them.
A can is a good example of a cylinder, so is a AA or AAA battery.
Memorize the formula for the volume of a cylinder.
To calculate the volume of a cylinder, you must know its height and the radius of the circular base (the distance from the center of the circle to its edge) at the top and bottom. The formula is V = πr
h, where V is the Volume, r is the radius of the circular base, h is the height, and π is the constant pi.
Understand what a regular pyramid is.
A pyramid is a three-dimensional shape with a polygon for a base, and lateral faces that taper at an apex (the point of the pyramid).
A regular pyramid is a pyramid in which the base of the pyramid is a regular polygon, meaning that all of the sides of the polygon are equal in length, and all of the angles are equal in measure.
We most commonly imagine a pyramid as having a square base, and sides that taper up to a single point, but the base of a pyramid can actually have 5, 6, or even 100 sides!
A pyramid with a circular base is called a cone, which will be discussed in the next method.
Learn the formula for the volume of a regular pyramid.
Learn the properties of a cone.
A cone is a 3-dimesional solid that has a circular base and a single vertex (the point of the cone). Another way to think of this is that a cone is a special pyramid that has a circular base.
If the vertex of the cone is directly above the center of the circular base, the cone is called a "right cone". If it is not directly over the center, the cone is called an "oblique cone." Fortunately, the formula for calculating the area of a cone is the same whether it is right or oblique.
Know the formula for calculating the volume of a cone.
The formula is V = 1/3πr
h, where r is the radius of the circular base of the cone, h is the height of the cone, and π is the constant pi, which can be rounded to 3.14.
A sphere is a perfectly round three-dimensional object, in which every point on the surface is an equal distance from the center. In other words, a sphere is a ball-shaped object.
Learn the formula for the volume of a sphere.
The formula for the volume of a sphere is V = 4/3πr
(stated: "four-thirds times pi r-cubed") where r is the radius of the sphere, and π is the constant pi (3.14).
Find the radius of the sphere.
If the radius is given in the diagram, then finding r is simply a matter of locating it. If the diameter is given, you must divide this number by 2 to find the radius. For example, the radius of the sphere in the diagram is 3 inches.
Worksheet and Practice Problems to Calculate Volume
How do you find the volume of a box?
Math Instructor, City College of San Francisco
The volume of a box is equal to the product of the three dimensions of the box. You would multiply the length, the width, and the height of the box to find its volume. Make sure the dimensions have the same unit. Some tricky questions give different units for each dimension.
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Volume is the measure of the capacity that an object holds. For example, if a cup can hold 100 ml of water up to the brim, its volume is said to be 100 ml. Volume can also be defined as the amount of space occupied by a 3-dimensional object.
The volume of an object is the amount of space occupied by the object or shape, which is in three-dimensional space. It is usually measured in terms of cubic units. In other words, the volume of any object or container is the capacity of the container to hold the amount of fluid (gas or liquid).
Volume calculator online - calculate the volume of common geometrical bodies such as cube, box, cylinder, sphere, cone, triangular prism. Quick and easy volume calculation with formulas included. Find the volume of three-dimensial bodies.
Volume is the amount of 3-dimensional space something takes up. Imagine how much water could be in it. Also called Capacity. Change the volume using the slider below: Units of volume include: Metric: cubic centimeters (cm 3), cubic meters (m 3), liters. US Standard: fluid ounce, cubic inch, cubic foot, pints, gallons.
