Calculating the Volume of a Cylinder Using π and Given Dimensions

Understanding cylinder volume is a fundamental concept in geometry, especially when dealing with circular shapes and their capacity measurements. A cylinder has a height (h) and a radius (r), and the volume (V) can be calculated using the formula V π r2 h. In this guide, we will walk through the solution for a specific cylinder with a height of 14 ft and a radius of 5 ft, using 3.14 as an approximation for π.

Identifying the Cylinder's Dimensions and the Formula to Use

The problem at hand is to find the volume of a cylinder with a height of 14 ft and a radius of 5 ft. The general formula for the volume of a cylinder is given by V π r2 h. Here, π (pi) is approximately 3.14, r is the radius, and h is the height of the cylinder.

Calculating the Volume

Let's substitute the given dimensions into the formula to calculate the volume:

V 3.14 × (52) × 14

First, we calculate the square of the radius:

52 25

Now, multiply this value by the height:

25 × 14 350

Finally, multiply by π (3.14):

V 3.14 × 350 1099 cubic feet (ft3)

Therefore, the volume of the cylinder is approximately 1099 ft3.

Verifying the Calculation

To ensure the accuracy of the result, we can double-check the calculation. Using the same formula:

V 3.14 × (72) × 14

First, we calculate the square of the radius (72):

72 49

Then, multiply this value by the height (14):

49 × 14 686

Finally, multiply by π (3.14):

V 3.14 × 686 2154.04 cubic feet (ft3)

The more accurate result, using π as 22/7, would be:

V (22/7) × 49 × 14 2156 cubic feet (ft3)

While the first calculation was simpler and had a minor discrepancy, it is still a close estimate of the volume. The exact calculation yields a result of approximately 2154.04 ft3.

Order of Operations and Calculator Accuracy

When calculating the volume of a cylinder, it is important to follow the correct order of operations. If using a simple calculator, perform the square calculation first, then multiply the results by the height. Scientific calculators handle the order of operations automatically. Using 3.14 as an approximation for π, the volume of the cylinder can be calculated as follows:

V 3.14 × 72 × 14 3.14 × 49 × 14 2154.04 cubic feet (ft3)

Therefore, the volume of the cylinder is approximately 2154.04 cubic feet (ft3).