Calculating the Volume of a Cylinder Using Given Parameters

Understanding the properties of a cylinder can be crucial in various fields, including geometry, engineering, and design. One common task is to calculate the volume of a cylinder based on given parameters such as its base circumference and height. This article will guide you through the process using a specific problem: finding the volume of a cylinder with a base circumference of 18π cm, where the height is 5 cm less than 2/3 of its base diameter.

Given Data and Formulas

For this problem, we have the following data:

Base circumference of the cylinder: 18π cm Height is 5 cm less than 2/3 of the base diameter

The key formulas we will use are:

Base circumference formula: C 2πr Height calculation formula: h (2/3)d - 5 VOLUME FORMULA: V πr2h

Step-by-Step Calculation

1. Calculate the Radius

The base circumference (C) is given by the formula:

C 2πr

Given:

C 18π cm

Substitute and solve for r:

2πr 18π

Divide both sides by 2π:

r 18π / 2π 9 cm

2. Calculate the Diameter

The diameter (d) is:

d 2r 2 × 9 18 cm

3. Calculate the Height

The height (h) is given as 5 cm less than 2/3 of the base diameter:

h (2/3)d - 5

Substitute the base diameter:

h (2/3) × 18 - 5 12 - 5 7 cm

4. Calculate the Volume

The volume (V) of a cylinder is calculated using:

V πr2h

Substitute the values of r and h:

V π × 92 × 7 π × 81 × 7 567π cm3

Therefore, the volume of the cylinder is:

567π cm3

Conclusion

Using the given parameters, we have successfully calculated the volume of the cylinder. The key steps involved were first determining the radius and diameter from the base circumference, then calculating the height, and finally using the volume formula to find the volume. This method can be applied to similar problems in geometry and practical applications where the volume of a cylinder needs to be determined based on given parameters.