We are tasked with finding the volume of a circular can. This can is cylindrical in shape, meaning it has a circular base and straight sides. We are given the diameter of the can, which is 3 feet, and the height, which is 2 feet. To solve this problem, we need to apply the formula for calculating the volume of a cylind...
Key Concepts
The volume of a cylinder is the amount of space it occupies. It is calculated by multiplying the area of the base (a circle) by the height of the cylinder. Here are the key concepts involved:
1. Area of a Circle
The area of a circle is calculated using the formula:
Area = πr²
where:
- π (pi) is a mathematical constant approximately equal to 3.14159
- r is the radius of the circle
2. Radius and Diameter
The radius of a circle is the distance from the center of the circle to any point on its circumference. The diameter is the distance across the circle passing through its center. The diameter is twice the length of the radius.
Diameter = 2 * Radius
Calculation Steps
Now, let's calculate the volume of the circular can step by step:
1. Find the Radius
We are given the diameter of the can, which is 3 feet. To find the radius, we divide the diameter by 2:
Radius = Diameter / 2
Radius = 3 ft / 2
Radius = 1.5 ft
2. Calculate the Area of the Base
Using the formula for the area of a circle, we can calculate the area of the base:
Area = πr²
Area = 3.14159 * (1.5 ft)²
Area = 3.14159 * 2.25 sq ft
Area ≈ 7.06858 sq ft
3. Calculate the Volume
Finally, we multiply the area of the base by the height to find the volume:
Volume = Area of Base * Height
Volume = 7.06858 sq ft * 2 ft
Volume ≈ 14.13716 cubic ft
Conclusion
Therefore, the volume of the circular can with a diameter of 3 feet and a height of 2 feet is approximately 14.14 cubic feet. This calculation involves understanding basic geometric concepts and applying the appropriate formulas to solve the problem.