A steel cylinder has a length of 2.16 in, a radius of 0.22 in, and a mass of 41 g. What is the density of the steel in g/cm³?

Verified step by step guidance

1. Convert the length from inches to centimeters using the conversion factor 1 inch = 2.54 cm.
2. Convert the radius from inches to centimeters using the same conversion factor.
3. Calculate the volume of the cylinder using the formula for the volume of a cylinder: \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height (length).
4. Substitute the converted values of radius and height into the volume formula to find the volume in cubic centimeters.
5. Calculate the density using the formula \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \), where the mass is given in grams and the volume is in cubic centimeters.

Key Concepts

Density

Density is defined as the mass of an object divided by its volume. It is a physical property that indicates how much matter is contained in a given volume. The formula for density is ρ = m/V, where ρ is density, m is mass, and V is volume. Understanding density is crucial for determining how substances compare in terms of heaviness and buoyancy.

Volume of a Cylinder

The volume of a cylinder can be calculated using the formula V = πr²h, where r is the radius and h is the height (or length) of the cylinder. This formula is essential for finding the volume of the steel cylinder in the question, which is necessary to calculate its density. Knowing how to apply this formula allows for accurate volume calculations in various contexts.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. In this question, it is necessary to convert the dimensions of the cylinder from inches to centimeters to ensure that the density is expressed in g/cm³. Understanding how to perform unit conversions is vital in chemistry, as it allows for consistency and accuracy in measurements across different systems.