How to Determine Cubic Yards

Step-by-Step Guide

1. 1

   Step 1: Obtain all necessary measurements in yards.

   Cubic yard volumes can be obtained relatively easily for a variety of standard three-dimensional spaces via a few simple equations.
   
   However, these equations assume that all measurements have been taken in yards.
   
   Thus, before using one of these equations, it's important to ensure that you took your initial measurement(s) in yards or, alternatively, that you converted them into yards via a conversion factor.
   
   A few conversions for common measurements of length are below: 1 yard = 3 feet 1 yard = 36 inches 1 yard =
   0.914 meters 1 yard =
   91.44 centimeters
2. 2

   Step 2: Use the equation L × W × H for rectangular spaces.

   The volume of any rectangular three-dimensional space (rectangular prism, cuboid, etc.), can be determined simply by multiplying its length times its width times its height.
   
   This equation can also be thought of as multiplying the surface area of one of the rectangular space's faces by the dimension perpendicular to that face.
   
   For example, let's say we want to determine the volume (in yd3) of the dining room in our house.
   
   We measure the dining room to be 4 yd long, 3 yd wide, and
   2.5 yd high.
   
   To determine the room's volume, we simply multiply its length, width, and height: 4 × 3 ×
   2.5 = 12 ×
   2.5 =
   30.
   
   The room has a volume of 30 yd3.
   
   Cubes are rectangular spaces where all sides are equal in length.
   
   Thus, a cube's volume equation can be shortened from L × W × H to L3, etc. , Find the area of its circular face via the area equation for circles: multiply the mathematical constant pi (3.1415926...) by the circle's radius (the distance from the center of the circle to one of its edges) times itself.
   
   Then, simply multiply this answer by the height of the cylinder to find the cylinder's volume.
   
   As always, ensure all values are in yards.
   
   For example, let's say we want to determine the volume of a cylindrical hole in our back patio before installing a fountain.
   
   The hole is
   1.5 yards across and 1 yard deep.
   
   Divide the distance across the hole in half to get the hole's radius:
   0.75 yards.
   
   Then, multiply your variables according the the cylindrical volume equation: (3.14159) ×
   0.752 × 1 = (3.14159) ×
   0.5625 × 1 =
   1.767.
   
   The hole has a volume of
   1.767 yd3. , To calculate the volume of a sphere in cubic yards, all you need to know is its radius
   - the distance from its center to its outside edge
   - in yards.
   
   Simply cube this number (multiply it by itself two times), then multiply it by 4/3 pi to get the sphere's volume in cubic yards.
   
   For example, let's say we want to find the volume inside a spherical hot air balloon.
   
   The hot air balloon is 10 yards across.
   
   Divide 10 in half to find the balloon's radius
   - 5 yards.
   
   Then, simply plug this into the equation for "R" as follows: 4/3 pi × (5)3 = 4/3 (3.14159) × 125 =
   4.189 × 125 =
   523.6.
   
   There are
   523.6 yd3 in the balloon. , Simply find the height and radius of a cone (in yards), then solve as if finding the volume of a cylinder.
   
   Multiply your result by 1/3 to get the volume of your cone.
   
   For example, let's say that we want to find the volume of an ice cream cone.
   
   The ice cream cone is fairly small
   - it has a radius of 1 inch and a height of 5 inches.
   
   Converted to yards, these are .028 yards and .139 yards, respectively.
   
   Solve as follows: 1/3 (3.14159) × .0282 × .139 = 1/3 (3.14159) ×
   0.000784 × .139 = 1/3 ×
   0.000342 =
   1.141-4.
   
   There are
   1.141-4 yd3 in the ice cream cone. , When confronted with a three-dimensional shape that doesn't have an elegant equation for its volume, try to break the space up into multiple spaces whose volume (in cubic yards) can be more easily calculated.
   
   Then, find the volume of these spaces individually, adding your results to find the final volume value.
   
   Let's say, for instance, that we want to find the volume of a small grain silo.
   
   The silo has a cylindrical body 12 yards high with a radius of
   1.5 yards.
   
   The silo also has a conic roof that is 1 yard high.
   
   By calculating the volume of the roof and the body of the silo separately, we can find the silo's total volume:
   Pi × R2 × H + 1/3 Pi × R'2 × H' (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 silo has a volume of
   87.178 cubic yards.
3. 3

   Step 3: For cylindrical spaces

4. 4

   Step 4: use the equation pi × R2 × H. Finding the volume of a cylindrical space is simply a matter of multiplying the two-dimensional area of one of its circular faces by the height or length of the cylinder.

5. 5

   Step 5: For spheres

6. 6

   Step 6: use the equation 4/3 pi × R3.

7. 7

   Step 7: For cones

8. 8

   Step 8: use the equation 1/3 pi × R2 × H. The volume of a given cone is 1/3 the volume of a cylinder that has the same height and radius as the cone.

9. 9

   Step 9: For irregular shapes

10. 10

    Step 10: try using multiple equations.

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