Calculating the Volume of a Circular Post in Cubic Feet

Suppose a circular post has a diameter of 20 cm and is 180 cm long. In this article, we will calculate its volume in cubic feet. We will approach this task using two methods: one involving a conversion from metric to Imperial units, and the other performing all calculations in Imperial units before converting the final result.

Assumptions

For the purpose of this calculation, we assume that the base and top of the post are cut at right angles to the sides, and that the diameter remains consistent throughout the length of the post.

Analysis and Calculation

Method 1: Convert all Imperial Units to Metric, then Calculate

First, let's convert the given dimensions from Imperial units to metric units for a more straightforward calculation.

1 cm 0.394 inches 1 foot 30.48 cm 1 cm3 0.00003531414667 ft3

The post's diameter is 20 cm, so the radius is 10 cm.

Step 1: Calculate the Area of the Base

The area of the base of the post is given by the formula: Abase π r2.

Using π ≈ 3.141593, the area of the base is:

Abase 3.141593 × (102) 3.141593 × 100 314.1593 cm2

Step 2: Calculate the Volume in Cubic Centimeters

The volume of the post in cubic centimeters is the area of the base multiplied by the height:

V Abase × height 314.1593 cm2 × 180 cm 56,548.7 cm3

Step 3: Convert the Volume to Cubic Feet

Now, we convert the volume from cubic centimeters to cubic feet:

V (ft3) 56,548.7 cm3 × 0.00003531414667 ft3/cm3 ≈ 1.9970 ft3

Method 2: Perform All Calculations in Imperial Units, Then Convert

Step 1: Calculate the Radius and Area in Inches

The diameter of the post is 18 inches (since 180 cm / 30.48 cm/inch 5.9055 inches).

The radius in inches is half the diameter, so:

r 18/2 9 inches

The area of the base in square inches is:

Abase π r2 3.141593 × (92) 3.141593 × 81 ≈ 254.469 inches2

Step 2: Calculate the Volume in Cubic Inches

The volume in cubic inches is:

V (in3) Abase × height 254.469 in2 × 18 in ≈ 4,580.44 in3

Step 3: Convert the Volume to Cubic Feet

Finally, convert the volume from cubic inches to cubic feet:

V (ft3) 4,580.44 in3 × (1/1728) ft3/in3 ≈ 1.9970 ft3

Conclusion

Both methods yielded the same result: the volume of the post is approximately 1.9970 cubic feet. This calculation helps us understand how to approach similar problems involving unit conversions and volume calculations for circular objects.

Keywords

circular post, volume calculation, unit conversion.