How to find the volume of a can?

Understand the Problem

The question is asking for the method to calculate the volume of a cylindrical can, which typically involves using the formula for the volume of a cylinder: V = πr²h, where r is the radius and h is the height of the can.

Answer

The volume of a cylindrical can is calculated using the formula $V = \pi r^2 h$.

Steps to Solve

Identify the Formula
To calculate the volume of a cylindrical can, we will use the formula: $$ V = \pi r^2 h $$
where ( V ) is the volume, ( r ) is the radius, and ( h ) is the height.
Determine the Radius and Height
Identify the values for the radius ( r ) and the height ( h ) of the cylindrical can. Make sure both values are in the same unit (e.g., inches, centimeters).
Substitute Values into the Formula
Insert the values of ( r ) and ( h ) into the formula. For example, if the radius is 3 cm and the height is 5 cm, the formula becomes: $$ V = \pi (3)^2 (5) $$
Calculate the Volume
Perform the square operation and then multiply by the height and ( \pi ). Continuing with our example: $$ V = \pi (9) (5) = 45\pi $$
Provide the Final Answer
Lastly, calculate or approximate the volume using the approximate value of ( \pi ) (3.14 or 3.14159) if needed. For our example: $$ V \approx 45 \times 3.14 \approx 141.3 \text{ cm}^3 $$

The volume of the cylindrical can is given by the formula: $$ V = \pi r^2 h $$
where you substitute the specific values for ( r ) and ( h ).

More Information

The volume formula for a cylinder can be used in various real-life applications, such as calculating the capacity of cans, pipes, and many other cylindrical objects. Understanding this formula helps in fields such as engineering, manufacturing, and environmental science.

Tips

Confusing radius and diameter: Remember that the radius is half the diameter. Always use the radius in the formula.
Using different units for radius and height: Ensure both measurements are in the same units before substituting into the formula.

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