Cubic yards (abbreviated yd3) is a unit of measurement of volume equal to the volume of a cube whose sides are exactly 1 yard or about 764.5 liters. The cubic yard is a unit of measurement that is widely used for various types of work and practical activities, for example when pouring concrete in a construction project. For a rectangular shape with length P, width L, and height T, the volume in cubic yards can be easily found using the equation Volume = W × L × H, provided that P, L, and T are measured in yards.
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Method 1 of 2: Finding the Volume of a 3-Dimensional Building
Step 1. Find all required measurements in yards
The volume of cubic yards for a variety of standard three-dimensional shapes can be found easily using a few simple equations. However, these equations can only be used if all measurements are made in yards. Thus, before using any of these equations, it's important to make sure that you take your initial measurements in yards or that you convert the measurements to yards using a conversion factor. Here are some common measurement conversions for length:
- 1 yard = 3 feet
- 1 yard = 36 inches
- 1 yard = 0.914 meters
- 1 yard = 91.44 centimeters
Step 2. Use the equation P × L × T to construct a rectangular space
The volume of any three-dimensional shape of a quadrilateral (rectangular prism, cube, etc.) can be found simply by multiplying its length, width, and height. This equation can also be thought of as multiplying the surface area of one side of a rectangle of a shape by the dimension that is perpendicular to that side.
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For example, let's say we want to find the volume (in yd3) from the dining room in our house. The dining area is 4 yd long, 3 yd wide, and 2.5 yd high. To find the volume of a room, we just need to multiply the length, width and height:
- 4 × 3 × 2, 5
- = 12 × 2, 5
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= 30. The room has volume 30 yd3.
- A cube is a quadrilateral whose all sides are the same length. Thus, the equation for finding the volume of a cube can be simplified from P × L × T to P3, etc.
Step 3. To construct a cylindrical space, use the equation pi × R2 × T.
Finding the volume of a cylindrical shape can be done by multiplying the two-dimensional area of one side of the circle by the height or length of the cylinder. Find the area of the circle's side using the area equation for the circle: multiply the mathematical constant pi (3, 1415926…) by the circle's radius (distance from the circle's center to one of its sides) squared. Then, just multiply this answer by the height of the cylinder to find the volume of the cylinder. As always, make sure that all values are in yards.
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For example, let's say we want to find the volume of a tubular hole on our back porch before installing a fountain. The holes are 1.5 yards across and 1 yard deep. Divide the length of the hole by two to get the radius of the hole, which is 0.75 yards. Then, multiply your variables according to the equation for the volume of the cylinder:
- (3, 14159) × 0, 752 × 1
- = (3, 14159) × 0, 5625 × 1
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= 1,767. The hole has a volume 1,767 yd3.
Step 4. For spheres, use the equation 4/3 pi × R3.
To calculate the volume of a sphere in cubic yards, all you need to know is its radius, which is the distance from the center of the circle to its outer edge in yards. Then, multiply this number by three (multiply by itself twice), and multiply the result by 4/3 pi to get the volume of the sphere in cubic yards.
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For example, let's say we want to find the volume of a spherical hot air balloon. The transverse length of the hot air balloon is 10 yards. Divide 10 by two to get the radius of the balloon, which is 5 yards. Then, just plug this number for the value of "R" into an equation like this:
- 4/3 pi × (5)3
- = 4/3 (3, 14159) × 125
- = 4, 189 × 125
- = 523, 6. The volume of the balloon is 523, 6 yd3.
Step 5. For the cone, use the 1/3 pi × R. equation2 × T.
The volume of a cone is 1/3 the volume of a cylinder that has the same height and radius as the cone. Just find the height and radius of the cone (in yards), then solve the equation like finding the volume of a cylinder. Multiply the result by 1/3 to get the volume of your cone.
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For example, let's say we want to find the volume of an ice cream cone. The ice cream cone is quite small and has a radius of 1 inch and a height of 5 inches. Converted to yards, the radius is 0.028 yards and the height is 0.139 yards. Solve as follows:
- 1/3 (3, 14159) × 0, 0282 × 0, 139
- = 1/3 (3, 14159) × 0, 000784 × 0, 139
- = 1/3 × 0, 000342
- = 1, 141-4. The volume of the ice cream cone is 1, 141-4.
Step 6. For irregular shapes, try using some equations
When working on a three-dimensional figure that doesn't have a fixed equation to find its volume, try dividing the shape into several shapes whose volume (in cubic yards) is easier to calculate. Then, find the volume of the shapes of the space separately. Add the volumes of the shapes to find the final volume.
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Suppose, we want to find the volume of a small barn of wheat. This barn has a tubular body 12 yards high and 1.5 yards radius. The barn also has a 1-yard-high conical roof. By calculating the volumes of the roof and body of the barn separately, we can find the total volume of the barn:
- pi × R2 × H + 1/3 pi × R'2 × T'
- (3, 14159) × 1, 52 × 12 + 1/3 (3, 14159) × 1, 52 × 1
- = (3, 14159) × 2, 25 × 12 + 1/3 (3, 14159) × 2, 25 × 1
- = (3, 14159) × 27 + 1/3 (3, 14159) × 2, 25
- = 84, 822 + 2, 356
- = 87, 178. The barn has a volume 87, 178 cubic yards.
Method 2 of 2: Quick Trick to Find Cubic Yards of Cast Concrete
Step 1. Find the size of the mold area that you will pour the concrete into
For example, when pouring cast-iron to make a concrete patio, you usually pour the cast-concrete into a mold several inches to a foot high. In this case, you don't need to use complicated formulas to find the volume of cast concrete you need. Instead, use contractor tricks to quickly figure out the amount of cast concrete you need. Start by finding the size of the mold area that you will be pouring the concrete into.
- Remember – for area, we measure in feet, not yards, as above.
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As a reminder, for squares or rectangles, this area can be found by multiplying Length × Width.
For a circle, the formula is Pi × R2.
For more complex shapes, look up the many guides to calculating surface area on wikiHow.
Step 2. Know the thickness of the concrete you want
It's simple – just measure the depth of the mold you're pouring with the concrete. Since we're pouring it into a fairly shallow mold, we can calculate our measurements in cm or inches instead of measuring them in the cumbersome m or feet.
Step 3. Divide your area measurement by the coefficient based on the thickness of your concrete cast
All you have to do to calculate the cubic yards of your concrete cast is to divide your area measurement number by a certain number. If your cast concrete needs to be thin, this number will get bigger. If your cast concrete needs to be thick, this number will get smaller. See below for commonly used thicknesses or continue to the next step if your thickness doesn't match one of the following:
- If the concrete is 4 inches thick, divide the area by 81 to calculate cubic yards.
- If the concrete is 6 inches thick, divide the area by 54 to calculate cubic yards.
- If the concrete is 8 inches thick, divide the area by 40 to calculate cubic yards.
- If the concrete is 12 inches thick, divide the area by 27 to calculate cubic yards.
Step 4. Determine the unusual thickness with a simple formula
If your thickness doesn't match the above examples, don't worry – it's easy to find the volume of cast concrete you need. Just divide 324 by your concrete cast thickness (in inches). Then, multiply the answer by your area measurement to find the total cubic yards of cast concrete.
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Suppose our concrete cast for an area of 10 feet × 10 feet should be 3.5 inches thick. In this case, we'll find our cubic yards as follows:
- 324/3, 5 = 92, 6
- 10 × 10 = 100
- 100/92, 6 = 1, 08. We need 1, 08 yd3 cast concrete.
Step 5. Buy more cast concrete than you need
When pouring cast concrete, it's usually a good idea to buy more cast concrete just in case your measurements aren't quite right. After all, dry concrete mix that you don't end up using can be stored and used for other projects. However, if you don't have enough cast concrete, you'll be in trouble. Someone may have to run to the hardware store before you can proceed with the project. So, make sure to buy more cast concrete, especially for big projects.
