Cubic area formula

Cubic area formula DEFAULT

Cubic Feet Calculator

How to calculate cubic feet

Cubic feet is a unit of volume. To calculate the volume or capacity of an item or space in cubic feet you will first need to measure its length, width and height in either feet, inches (or a combo of both), centimeters, meters or yards. Once you have those measurements, you apply some multiplication as follows...

Calculating cubic feet for different units (formulae)

  • From feet: length (ft) × width (ft) × height (ft) = cubic feet
  • From inches: length (in) × width (in) × height (in) ÷ 1728 = cubic feet
  • From yards: length (yd) × width (yd) × height (yd) × 27 = cubic feet
  • From cm: length (cm) × width (cm) × height (cm) ÷ 28316.85 = cubic feet
  • From meters: length (m) × width (m) × height (m) × 35.314667 = cubic feet
Diagram of how to calculate cubic feet

Let's look at each of these in turn.

Calculating cubic feet from measurements in feet

If you have measured the width, length and height of your item in feet then the calculation process is straight forward: Simply multiply the 3 figures together.

As an example, let's say you're looking for the capacity of a box that measures 5ft by 3ft by 2ft. Multiplying those 3 figures together gives you a total cubic feet value of 30ft3.

Should you have already calculated your square footage, you simply need to multiply this figure by the height measurement.

If you're looking to measure a refrigerator, take a look at our article, how many cubic feet is my refrigerator?

Calculating cubic feet from inches

If you have measured the dimensions of your item in inches then do the following:

  1. Multiply your length, width and height figures together, giving you a total in cubic inches (in3)
  2. Divide the total by 1728 (as there are 1728 cubic inches in a cubic foot).

As an example, let's say you're looking for the capacity of a box that measures 55" x 30" x 15". Multiplying those 3 figures together gives you a total cubic inches value of 24750in3. To convert that figure to cubic feet we divide it by 1728, giving a total of 14.323ft3.

Calculating cubic feet from centimeters

If you have measured the dimensions of your item in centimeters (cm) then do the following:

  1. Multiply your length, width and height figures together, giving you a total in cubic centimeters (cm3)
  2. Divide the total by 28,316.85 (as there are approximately 28,316.85 cubic cm in a cubic foot).

Calculating cubic feet from yards

If you have measured the dimensions of your item in yards then do the following:

  1. Multiply your length, width and height figures together, giving you a total in cubic yards (yd3)
  2. Multiply the total by 27 (as there are 27 cubic feet in a cubic yard).

Once you have your resulting figure, check it against the calculator at the top of this page. As an alternative, if you've taken your measurements and want to convert them to cubic yards, give the cubic yards calculator a try.

You can learn more about how to calculate cubic feet in this article.


How to convert from cubic inches to cubic feet

One cubic foot equals 1728 cubic inches. So, to convert from cubic inches to cubic feet you should divide your cubic inches figure by 1728. Should you not wish to do this manually, give my volume converter a try.


If you have any problems using this cubic feet calculator, please contact me.


Sours: https://www.thecalculatorsite.com/misc/cubic-feet-calculator.php

This page explains how to calculate the volume of solid objects, i.e. how much you could fit into an object if, for example, you filled it with a liquid.

Area is the measure of how much space there is within a two dimensional object (see our page: Calculating Area for more).

Volume is the measure of how much space there is within a three-dimensional object. Our page on three-dimensional shapes explains the basics of such shapes.

In the real world, calculating volume is probably not something that you will use as often as calculating area.

However it can still be important. Being able to calculate volume will enable you to, for example, work out how much packing space you have when moving house, how much office space you need, or how much jam you can fit into a jar.

It can also be useful for understanding what the media mean when they talk about the capacity of a dam or the flow of a river.

Calculating Area and Volume. Area is measured in units squared, how many squares will fit into a flat (two dimensional space)?   Volume is measured in units cubed, how many cubes will fit into a solid (three-dimensional) object?

A Note on Units


Area is expressed in square units (2), because it is it is measured in two dimensions (e.g. length × width).

Volume is expressed in cubic units (3), because it is measured in three dimensions (e.g. length × width × depth). Cubic units include cm3, m3 and cubic feet. Cubic units include cm3, m3 and cubic feet.

WARNING!

Volume can also be expressed as liquid capacity.

Metric System

In the metric system liquid capacity is measured in litres, which is directly comparable with the cubic measurement, since 1ml = 1cm3. 1 litre = 1,000 ml = 1,000cm3.

Imperial/English System

In the imperial/English system the equivalent measurements are fluid ounces, pints, quarts and gallons, which are not easily translated into cubic feet. It is therefore best to stick to either liquid or solid volume units.

For more, see our page on Systems of Measurement.


Basic Formulae for Calculating Volume

Volume of Rectangle-Based Solids

Area = Width x Length. Volume = Width x Length x Height.

Whereas the basic formula for the area of a rectangular shape is length × width, the basic formula for volume is length × width × height.

How you refer to the different dimensions does not change the calculation: you may, for example, use 'depth' instead of 'height'. The important thing is that the three dimensions are multiplied together. You can multiply in which-ever order you like as it won't change the answer (see our page on multiplication for more).

A box with the dimensions 15cm width, 25cm length and 5 cm height has a volume of:
15 × 25 × 5 = 1875cm3

Volume of Prisms and Cylinders

This basic formula can be extended to cover the volume of cylinders and prisms too. Instead of a rectangular end, you simply have another shape: a circle for cylinders, a triangle, hexagon or, indeed, any other polygon for a prism.

Effectively, for cylinders and prisms, the volume is the area of one side multiplied by the depth or height of the shape.

The basic formula for volume of prisms and cylinders is therefore:

Area of the end shape × the height/depth of the prism/cylinder.

Watch out for inconsistent units!


A straight length of circular pipe has an internal diameter of 2cm and a length of 1.7m. Calculate the volume of water in the pipe.

In this example you need to calculate the volume of a very long, thin cylinder, that forms the inside of the pipe. The area of one end can be calculated using the formula for the area of a circle πr2. The diameter is 2cm, so the radius is 1cm. The area is therefore π × 12, which is 3.14cm2.

The length of the pipe is 1.7m, so you need to multiply the end area by the length in order to find the volume.

Watch out for inconsistent units! The area is in centimetres, but the length is in metres. First convert the length into cm 1.7 × 1000 = 1700cm.

The volume is therefore 3.14 × 1700 = 5338 cm3. This is equivalent to 5.338 litres, or 0.0053 m3.


Volume of Cones and Pyramids

The same principle as above (width × length × height) holds for calculating the volume of a cone or a pyramid except that, because they come to a point, the volume is only a proportion of the total that it would be if they continued in the same shape (cross-section) right through.

The volume of a cone or pyramid is exactly one third of what it would be for a box or cylinder with the same base.

The formula is therefore:

Area of the base or end shape × the height of the cone/pyramid × 1/3

Refer back to our page Calculating Area if you cannot remember how to calculate the area of a circle or triangle.

For example, to calculate the volume of a cone with a radius of 5cm and a height of 10cm:

The area within a circle = πr2 (where π (pi) is approximately 3.14 and r is the radius of the circle).

In this example, area of base (circle) = πr2 = 3.14 × 5 × 5 = 78.5cm2.

78.5 × 10 = 785

785 × 1/3 = 261.6667cm3

Calculate the volume of a sphere. 4/3 x pi x radius cubed.

Volume of a Sphere

As with a circle, you need π (pi) to calculate the volume of a sphere.

The formula is 4/3 × π × radius3.

You may be wondering how you could work out the radius of a ball. Short of sticking a knitting needle through it (effective, but terminal for the ball!), there is a simpler way.

You can measure the distance around the widest point of the sphere directly, for example, with a tape measure. This circle is the circumference and has the same radius as the sphere itself.

The circumference of a circle is calculated as 2 x π x radius.

To calculate the radius from the circumference you:

Divide the circumference by (2 x π).


Worked Examples: Calculating Volume


Example 1

Cylinder with length of 20cm and radius of 2.5cm
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 πr2× radius × radius). π (pi) 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




Sphere with a radius of 2cm and pyramid with a square base of 2.5cm and a height of 10cm.

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 × π × 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.



Calculating the Volume of Irregular Solids

Just as you can calculate the area of irregular two-dimensional shapes by breaking them down into regular ones, you can do the same to calculate the volume of irregular solids. Just split the solid up into smaller parts until you reach only polyhedrons that you can work with easily.


Worked example

Calculate the volume of a water cylinder with total height 1m, diameter of 40cm, and whose top section is hemispherical (half of a sphere).
Irregular solid. Circular base with a diameter of 40cm and with a total height of 1m. Top section is semi-spherical.

You first divide the shape into two sections, a cylinder and a hemisphere.

The volume of a sphere is 4/3 × π × radius3. In this example the radius is 20cm (half the diameter). Because the top is hemispherical, its volume will be half that of a full sphere. The volume of this section of the shape therefore:

 0.5 × 4/3 × π × 203 = 16,755.16cm3

The volume of a cylinder is area of the base × height. Here, the height of the cylinder is the total height less the radius of the sphere, which is 1m – 20cm = 80cm. The area of the base is πr2.

The volume of the cylindrical section of this shape is therefore:

80 × π × 20 × 20 = 100,530.96cm3

The total volume of this water container is therefore:
100,530.96 + 16,755.16 = 117,286.12cm3.

This is quite a large number, so you may prefer to convert it to 117.19 litres by dividing by 1,000 (since there are 1000cm3 in a litre). However, it is quite correct to express it as cm3 since the problem does not ask for the answer to be expressed in any particular form.




Understanding Geometry - The Skills You Need Guide to Numeracy

Further Reading from Skills You Need


Understanding Geometry
Part of The Skills You Need Guide to Numeracy

This eBook covers the basics of geometry and looks at the properties of shapes, lines and solids. These concepts are built up through the book, with worked examples and opportunities for you to practise your new skills.

Whether you want to brush up on your basics, or help your children with their learning, this is the book for you.


In Conclusion…

Using these principles, if necessary, you should now be able to calculate the volume of almost anything in your life, whether that’s a packing crate, a room, or a water cylinder.

Sours: https://www.skillsyouneed.com/num/volume.html
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How to Calculate the Area of a Cube

A cube is a simple shape, and it would make sense to assume there is a simple formula for computing its surface area. All sides of a cube have the same length, and all the faces have the same area. Since a cube has six faces, all you have to do is calculate the area of one face and multiply by 6 to find the total surface area. The mathematical formula that results from this discussion is: For a cube with sides of length ​L​, the surface area

A = 6L^2

Area of a Square

A cube is made from squares, and a square is a special type of rectangle. You find the area of any rectangle by multiplying the length of its longer side by that of its shorter side. When the rectangle becomes a square, all four sides have the same length, so you simply multiply the length by itself. In other words, you square the length:

L × L = L^2

Surface Area of a Cube

The surface area of a cube can be a useful thing to know. For example, someone designing a 3-D solar collector needs to know how many solar cells will fit on its surface. The answer depends on surface area.

To find surface area, first compute the area of one face, which is simply ​L2. The total surface area is the area of all six faces, so that would be

A = 6L^2

Example

One die from a pair of dice is half an inch high. What is its surface area?

Dice are cubic, so first find the area of one face. You know the side of one face is 0.5 inches, so

0.5^2 = 0.25

There are six faces on the die, so multiply that area (0.25) by 6 to get the surface area of the cube:

A = 6 × 0.25 = 1.5 \text{ inches}^2

References

About the Author

Chris Deziel holds a Bachelor's degree in physics and a Master's degree in Humanities, He has taught science, math and English at the university level, both in his native Canada and in Japan. He began writing online in 2010, offering information in scientific, cultural and practical topics. His writing covers science, math and home improvement and design, as well as religion and the oriental healing arts.

Sours: https://sciencing.com/calculate-area-cube-5137293.html

Learning Outcomes

  • Find the volume and surface area of a cube

 

A cube is a rectangular solid whose length, width, and height are equal. See Volume and Surface Area of a Cube, below. Substituting, s for the length, width and height into the formulas for volume and surface area of a rectangular solid, we get:

[latex]\begin{array}{ccccc}V=LWH\hfill & & & & S=2LH+2LW+2WH\hfill \\ V=s\cdot s\cdot s\hfill & & & & S=2s\cdot s+2s\cdot s+2s\cdot s\hfill \\ V={s}^{3}\hfill & & & & S=2{s}^{2}+2{s}^{2}+2{s}^{2}\hfill \\ & & & & S=6{s}^{2}\hfill \end{array}[/latex]
So for a cube, the formulas for volume and surface area are [latex]V={s}^{3}[/latex] and [latex]S=6{s}^{2}[/latex].

Volume and Surface Area of a Cube

For any cube with sides of length [latex]s[/latex],

An image of a cube is shown. Each side is labeled s. Beside this is Volume: V equals s cubed. Below that is Surface Area: S equals 6 times s squared.

 

example

A cube is [latex]2.5[/latex] inches on each side. Find its 1. volume and 2. surface area.

Solution
Step 1 is the same for both 1. and 2., so we will show it just once.

Step 1. Read the problem. Draw the figure and

label it with the given information.

.
1.
Step 2. Identify what you are looking for.the volume of the cube
Step 3. Name. Choose a variable to represent it.let V = volume
Step 4. Translate.

Write the appropriate formula.

[latex]V={s}^{3}[/latex]
Step 5. Solve. Substitute and solve.[latex]V={\left(2.5\right)}^{3}[/latex]

[latex]V=15.625[/latex]

Step 6. Check: Check your work.
Step 7. Answer the question.The volume is [latex]15.625[/latex] cubic inches.
2.
Step 2. Identify what you are looking for.the surface area of the cube
Step 3. Name. Choose a variable to represent it.let S = surface area
Step 4. Translate.

Write the appropriate formula.

[latex]S=6{s}^{2}[/latex]
Step 5. Solve. Substitute and solve.[latex]S=6\cdot {\left(2.5\right)}^{2}[/latex]

[latex]S=37.5[/latex]

Step 6. Check: The check is left to you.
Step 7. Answer the question.The surface area is [latex]37.5[/latex] square inches.

 

try it

 

example

A notepad cube measures [latex]2[/latex] inches on each side. Find its 1. volume and 2. surface area.

Show Solution

Solution

Step 1. Read the problem. Draw the figure and

label it with the given information.

.
1.
Step 2. Identify what you are looking for.the volume of the cube
Step 3. Name. Choose a variable to represent it.let V = volume
Step 4. Translate.

Write the appropriate formula.

[latex]V={s}^{3}[/latex]
Step 5. Solve the equation.[latex]V={2}^{3}[/latex]

[latex]V=8[/latex]

Step 6. Check: Check that you did the calculations

correctly.

Step 7. Answer the question.The volume is [latex]8[/latex] cubic inches.
2.
Step 2. Identify what you are looking for.the surface area of the cube
Step 3. Name. Choose a variable to represent it.let S = surface area
Step 4. Translate.

Write the appropriate formula.

[latex]S=6{s}^{2}[/latex]
Step 5. Solve the equation.[latex]S=6\cdot {2}^{2}[/latex]

[latex]S=24[/latex]

Step 6. Check: The check is left to you.
Step 7. Answer the question.The surface area is [latex]24[/latex] square inches.

 

try it

 

Sours: https://courses.lumenlearning.com/prealgebra/chapter/finding-the-volume-and-surface-area-of-a-cube/

Area formula cubic

Surface Area of a Cube

Companies package items in boxes use surface area to determine how much cardboard would be needed to make the box. This is important for determining the amount they need to make the boxes and in determining the cost.



In order to calculate the surface area, we need to include the area of every side of the box. Each side of a cube happens to be a square that is the same as each of the other squares used to make the cube.



This makes calculating the surface area very simple. Determine the area of one of the squares using the formula A = s2. Then multiply by 6 because there are 6 congruent sides.



Let's try it out!
  Be sure to complete the exponent before multiplying by 6!






The area of the blue cube is 150 square centimeters.



Example:

Determine the surface area of the cube.


Solution:
  If working with fraction is difficult for you, convert to a decimal!








The surface area of this cube is 37.5 square inches.

If you know the surface area you can also work backwards to determine the side lengths.

Example:The surface area of a cube is 86.64 square meters. Determine the side length of the cube.

Solution:Because we already know the surface area, we can work backwards through the steps to determine the length of the side.

The side length was squaredand then multiplied by 6. So we will divide by 6to undo the multiplying. Then we will take the square rootto undo the squaring.



Therefore, the sides of the cube are each 3.8 meters long.

Example:The surface area of a cube is 384 m2. Determine the volume of the cube. Solution: We need to know the side length in order to determine the volume. So the first step is to work backwards from the surface area of the side length.



The side length of the cube is 8 meters.

Now use this value to determine the volume using the formula V = s3.

The volume of the cube is 512 cubic meters.

Let's Review

To determine the surface area of a cube, calculate the area of one of the square sides, then multiply by 6 because there are 6 sides. This is the same as solving using the formula SA = 6s2. If you are given the surface area, you can determine the side length by working backwards. Take the surface area and work backwards by dividing by 6 and then take the square root.

Sours: https://www.softschools.com/math/geometry/topics/surface_area_of_a_cube/
How To Calculate The Volume In Cubic Feet \u0026 Cubic Meters

Surface Area of Cube

FAQs on Surface Area of Cube

What Is Meant By the Surface Area of a Cube?

The surface area of a cube is defined as the total area covered by the surfaces of a cube. To calculate the surface area of a cube, we find the sum of the area of surfaces. 

What Is the Surface Area of Cube Formula?

The surface area of a cube with edge length as 'a' can be calculated using the following formulas, LSA of Cube = 4a2 and, TSA of Cube = 6a2.

What Is the Unit Used to Express Surface Area of Cube?

Surface area of a cube is expressed in square units, for example using units like in2, ft2, yd2, m2, cm2, etc.

What Is the Lateral Surface Area of a Cube?

The lateral area of a cube is the total area covered by the lateral or side surfaces of a cube. The formula to calculate lateral surface area of a cube is given as, Lateral surface area = 4a2, where, 'a' is the edge length of the cube.

What Is the Total Surface Area of Cube?

The total surface area of a cube is the area covered by all the six faces of a cube. The formula to find total surface area of a cube is given as, Total surface area = 6a2, where, 'a' is the edge length of the cube. 

What Is the Formula to Find the Area of the Base of a Cube?

The formula to find the area of the base of a cube is a2, where a is the length of the side of the cube.

Sours: https://www.cuemath.com/measurement/surface-area-of-cube/

You will also like:

(pi = pi = 3.141592...)

Volume Formulas

Note: "ab" means "a" multiplied by "b". "a2" means "a squared", which is the same as "a" times "a". "b3" means "b cubed", which is the same as "b" times "b" times "b".

Be careful!! Units count. Use the same units for all measurements. Examples

cube = a 3

rectangular prism = a b c

irregular prism = b h

cylinder = b h = pi r 2 h

pyramid = (1/3) b h

cone = (1/3) b h = 1/3 pi r 2 h

sphere = (4/3) pi r 3

ellipsoid = (4/3) pi r1 r2 r3

 

Units

Volume is measured in "cubic" units. The volume of a figure is the number of cubes required to fill it completely, like blocks in a box.

Volume of a cube = side times side times side. Since each side of a square is the same, it can simply be the length of one side cubed.

If a square has one side of 4 inches, the volume would be 4 inches times 4 inches times 4 inches, or 64 cubic inches. (Cubic inches can also be written in3.)

Be sure to use the same units for all measurements. You cannot multiply feet times inches times yards, it doesn't make a perfectly cubed measurement.

The volume of a rectangular prism is the length on the side times the width times the height. If the width is 4 inches, the length is 1 foot and the height is 3 feet, what is the volume?

NOT CORRECT .... 4 times 1 times 3 = 12

CORRECT.... 4 inches is the same as 1/3 feet. Volume is 1/3 feet times 1 foot times 3 feet = 1 cubic foot (or 1 cu. ft., or 1 ft3).

Sours: http://www.math.com/tables/geometry/volumes.htm


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