## Worked Examples: Calculating Volume

Example 1

Calculate the volume of a cylinder with a length of 20cm, and whose circular end has a radius of 2.5cm.

*First, work out the area of one of the circular ends of the cylinder.*

The area of a circle is r2 . is approximately 3.14.

The area of an end is therefore:

**3.14 x 2.5 x 2.5 = 19.63cm2**

The **volume** is the area of an end multiplied by the length, and is therefore:

**19.63cm2 x 20cm = 392.70cm3**

Example 2

Which is bigger by volume, a sphere with radius 2cm or a pyramid with base 2.5cm square and height of 10cm?

*First, work out the volume of the sphere**.*

The volume of a sphere is 4/3 × × radius3.

The volume of the sphere is therefore:

**4 ÷ 3 x 3.14 × 2 × 2 × 2 = 33.51cm3**

** Then work out the volume of the pyramid**.

The volume of a pyramid is 1/3 × area of base × height.

Area of base = length × breadth = 2.5cm × 2.5cm = 6.25cm2

Volume is therefore 1/3 x 6.25 × 10 = 20.83cm3

*The sphere is therefore larger by volume than the pyramid.*

## What Does Volume Mean In Shapes

Lesson Summary. Volume refers to the quantity of space that a 3-dimensional object occupies. Determining the volume of shapes can be done using certain formulas. The formulas for each of these shapes are: Cube volume equals s^3 where s is the side of the cube, V=s^3.

## What Is Volume Volume Definition

**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 is an SI unit for volume.

However, the term *volume* may also refer to many other things, such as

- the degree of loudness or the intensity of a sound
- the number or amount of something
- formal word for
*a book*or one in a set of related books.

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## Can You Do A Graph On A Ti

The first step in any graphing problem is to draw the graph. On the TI-83 and TI-84, this is done by going to the function screen by pressing the ?Y=? button and entering the function into one of the lines. After the function has been entered, press the ?GRAPH? button, and the calculator will draw the graph for you.

## Can You Change The Color Of The Graph On The Ti 84 Plus

If you?re graphing several functions on your TI-84 Plus calculator at once, your calculator automatically graphs each function in a different color. If you have the TI-84 Plus C, you may want to change the colors more to your liking or further distinguish your functions by choosing a different graph style. To do this, follow these steps:

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## What Are The Dimensions Of A Cube

A cube is a 3D object, so a cube has three dimensions:

**Length**Generally understood to be the larger of the flat dimensions.**Width**Generally understood to be the shorter of the flat dimensions.**Height or Depth**The dimension that brings the shape into our 3D world

Notice, we have two ways to describe the third dimension:

**Height**Use this term when the object rises before you, like a tall building.

**Depth**Use this term if the object drops beneath you, like a hole in the ground.

We need information about at least one of these three dimensions to measure the volume of a cube.

## Capacity In Relation To Volume

Capacity is the measure of the content of a vessel that holds liquids, grains, or other materials that take the shape of the container. Capacity is not necessarily the same as volume. It is always the interior volume of the vessel. Units of capacity include the liter, pint, and gallon, while the unit of volume is derived from a unit of length.

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## How To Find Volume

The volume formula **depends on the shape of the object**. One of the most popular shapes is a rectangular prism, also known as a box, where you can simply **multiply length times width times height** to find its volume. Another common shape is a cylinder to find its volume, multiply the height of the cylinder by the area of its base . For other 3D shapes, check Omni’s Volume Calculator.

## Calculating The Volume Of Rectangular Boxes

**Understand the volume of a rectangle equals it’s**If your box is a rectangular prism or a cube, the only information you need is the box’s length, width, and height. You can then multiply them together to get volume. This formula is often abbreviated as

*length*x*width*x*height.***V = l x w x h.**XResearch source

*Sample Question:*“If I have a box with a length of 10cm, width of 4cm, and height of 5cm, what is the volume of the box?”

*deep.*“XResearch source

**Measure the length of a box.**If your are looking down at your box, the top appears to be a flat rectangle/The length the longest side of this rectangle. Write this number down as “length.”XResearch source

**Measure the width of the box next to the length.**The width of the box is the other edge next to the length. If you are looking one side of the box, the width is the side the forms an “L” with the length. Write down this measurement as “width.”XResearch source

**Measure the height of the box.**This is the last side you have not measured, and is the distance from the top of the box to the ground. Write this measurement down as “height.”XResearch source

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## Does Volume Mean Add

Volume is **a measure of how much space an object takes up**. For example two shoe boxes together have twice the volume of a single box, because they take up twice the amount of space. … For example, in a cube we find the volume by multiplying the three side lengths together. In the cube above, the volume is 3×3×3 or 27.

## How Do I Use The Volume Calculator

Let’s look at the example of how to use this volume calculator:

**Select the 3D shape type**. If you can’t find the shape you want to calculate the volume of, choose other special dedicated calculators . In this example, let’s assume you want to calculate the volume of a cylinder.

**Choose the right section of the volume calculator**. In our case, it’s the part titled *Cylinder volume*.

**Type given data into proper boxes**. Our cylinder has a radius of 1 ft and a height of 3 ft. You can change the units by a simple click on the unit name.

**Here you go! The volume of a chosen shape is displayed**. In our case, it’s 9.42478 cu ft.

If you want to check how much that is in US barrels unit, just click on the unit name and choose barrels from the drop-down list. Our cylinder has a capacity of ~2.24 oil barrels.

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## How To Calculate Volume Volume Formulas

There is no simple answer to this question, as it depends on the shape of the object in question. Here are the formulas for some of the most common shapes:

Cube = s³, where *s* is the length of the side.

Sphere = r³, where *r* is the radius.

Cylinder = r²h, where *r* is the radius and *h* is the height.

Cone = r²h, where *r* is the radius and *h* is the height.

Rectangular solid = lwh, where *l* is the length, *w* is the width and *h* is the height .

Pyramid = Ah where *A* is a base area and *h* is the height. For a pyramid with a regular base, other equation may be used as well: Pyramid = * h * side_length² * cot, where *n* is a number of sides of the base for a regular polygon.

Prism = Ah, where *A* is a base area and *h* is the height. For a right triangular prism, the equation can be easily derived, as well as for a right rectangular prism, which is apparently the same shape as a box.

Shape |
---|

## How To Find The Volume Of A Rectangle Vs Volume Of A Box

**You can’t calculate a volume of a rectangle**, a volume of a circle or a volume of a square because they are 2-dimensional geometric figures. As such, a rectangle does not have a volume . What you’re probably looking for is the volume of a rectangular cuboid , which is a 3-dimensional object.

To find the volume of a box, simply multiply length, width, and height and you’re good to go! For example, if a box is 5×7×2 cm, then the volume of a box is 70 cubic centimeters.For dimensions that are relatively small whole numbers, calculating volume by hand is easy. For larger or decimal valued numbers, the use of the volume calculator is very efficient.

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## Calculating Different Shaped Boxes

**Find the volume of cylinders.**Cylinders are tubes, where the top and bottom are circles. To find volume of a cylinder, use the equation V = pi x r2 x h. Where pi = 3.14, r is the radius of the top circle, and h is the height.XResearch source

**Find the volume of a pyramid.**Pyramids have one side, or base, and all of the other sides comes to a point. To find volume, multiply the area of the base by the height, and then multiply that by the fraction 1/3. Thus, Volume of a Pyramid = 1/3.XResearch source

**Add the volume of the parts together to find the volume of complicated shapes.**For example, if I need to find the volume of an “L” shaped box, there are more than three sides to measure. If you view the box as two smaller boxes, however, you can find the volume of each smaller box and add them together to get the final volume. With our “L” shaped box, for example, we can view the vertical line as a rectangular box and the bottom horizontal line as a square box.XResearch source

## Discovering Formulas For Volume

Students who understand volume as it is described above can *reinvent* for themselves many of the volume formulas that they are often asked merely to memorize. Each formula they derive helps strengthen their understanding for the other formulas they know. The volume of a solid all of whose faces are rectangles is found, as shown above, by multiplying the lengths of each of its dimensions: the product of its two base dimensions gives the area of the base, the height tells how many layers are in it, and the product of all three gives the volume.

When the faces of the figure are not all rectangles, we can sometimes dissect the figure and reassemble the pieces into a solid whose faces *are* all rectangles.

This material is based upon work supported by the National Science Foundation under NSF Grant No. DRL-1934161 , NSF Grant No. DRL-1741792 , and NSF Grant No. ESI-0099093 .

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

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## How Do You Reset Programs On A Ti

Press the right arrow button twice to scroll right, then select ?1: All Memory.? Select ?2: Reset.? Your TI-84 calculator will erase all data, programs, and apps from the device. When complete, the screen will display ?RAM Cleared.? Your TI-84 will now be reset and restored to the original factory settings.

## How To Find The Volume Of A Solid

**The volume of a solid is the measure of how much space an object takes up. This article will show how to calculate the volume of a solid and the volume of regular and irregular solids.**

The method for determining the volume of solid depends on its shape. The volume of a solid is measured in cubic units, i.e., cubic centimeter, cubic meter, cubic feet, etc.

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## Volume Of A Cube Calculator

Are you looking for a free volume of a cube calculator to quickly solve problems? While we recommend learning how to solve problems without relying on a calculator, there are times when this tool can be very useful .

There are many cube volume calculator options available online, but we recommend Googles free calculator, which you can access by Googling volume of a cube calculator or

Note that Google used the letter ** a** instead of the letter

*s*.

## How To Calculate The Volume

Here are the steps to calculate volume of any solid shape:

- Identify all the given parameters that are useful and are required to substitute in the respective volume formula. Such as the radius to be ‘r’ and height to be ‘h’, the slant height, diameter, etc.
- Make sure all the parameters are of the same units.
- Substitute the values in the volume formula of the respective shapes.
- Write the units as cubic units.

Let us understand the steps with help of an example.

**Example: **Find the volume of a right circular cylinder of radius 25 m and height 1 meter. Use = 3.142.

**Solution:**

The radius of the cylinder is, r = 25 m.Its height is h = 1 meter.Its volume of cylinder is, V = r2h = 2 = 1963.75m3.The volume of a cylinder is 1963.75 cubic meters.

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## How To Calculate Volume Of A Box

This article was co-authored by Grace Imson, MA. Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University.There are 8 references cited in this article, which can be found at the bottom of the page. This article has been viewed 516,744 times.

Whether you need to mail a package or pass you next test, finding the volume of a box is easy. Volume is the measure of how big an object is in three dimensions, so the volume of a box measure how much room there is inside of the box. To find it, you need to make a few simple measurements of length, width, and height, and then multiply them.

## How Does The Volume Indicator Work

Understanding the Volume Price Trend Indicator The volume price trend indicator is **used to determine the balance between a security’s demand and supply**. The percentage change in the share price trend shows the relative supply or demand of a particular security, while volume indicates the force behind the trend.

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## Measuring Volume Of Liquids Solids And Gases

Because gases fill their containers, their volume is the same as the internal volume of the container. Liquids are commonly measured using containers, where the volume is marked or else is the internal shape of the container. Examples of instruments used to measure liquid volume include measuring cups, graduated cylinders, flasks, and beakers. There are formulas for calculating the volume of regular solid shapes. Another method of determining the volume of a solid is to measure how much liquid it displaces.

## Volume Of A Solid Formula

*Here are the volume formulas for different regular solids:*

**Rectangular prism**

The volume of a rectangular prism is equal to the product of base area and the height of the prism:

Volume of a solid rectangular prism = l x w x h

Since we know all sides or edges of a cube are equal in length, then a cubes volume is equal to any side, or edge cubed.

Volume of a cube = a³

The volume of a prism is equal to the base areas product and the height of a prism.

Volume of a prism = Base area x height

= B x h

The volume of a cylinder is equal to the area of its circular base and a cylinders height.

Volume of a cylinder = r²h

The volume of a pyramid is equal to one -third the product of its base area and its height.

Volume of a pyramid = 1/3Bh

For a square pyramid, the volume is given as:

Volume =1/3s²h

Where s is the side length of the base and h is the height of the pyramid.

**Rectangular pyramid**

The volume of a rectangular pyramid = 1/3 l w h

For a sphere, the volume is given as:

Volume of a sphere = 4/3 r³

Since a cone is a pyramid whose base is circular, therefore, the volume of a cone is:

Volume = 1/3 r²h

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