A cylindrical specimen of brass has a diameter of $20 \mathrm{mm}$ and a height of $100 \mathrm{mm}$. If its mass is $0.27 \mathrm{kg}$, what is the density of the brass in $\mathrm{kg}/m^3$?

• A. $5400$
• B. $8600$
• C. $3200$
• D. $2700$

Answer: (B)

Verified step by step guidance

1. Identify the given quantities: diameter (d) = 20 mm, height (h) = 100 mm, and mass (m) = 0.27 kg. Convert the dimensions from millimeters to meters for consistency in SI units: 1 mm = 0.001 m.
2. Calculate the radius (r) of the cylindrical specimen using the diameter: \(r = \frac{d}{2}\). Remember to use the converted value in meters.
3. Find the volume (V) of the cylinder using the formula for the volume of a cylinder: \(V = \pi r^{2} h\). Use the radius and height in meters to get the volume in cubic meters.
4. Calculate the density (\rho) using the formula: \(\rho = \frac{m}{V}\), where m is the mass in kilograms and V is the volume in cubic meters.
5. Substitute the values of mass and volume into the density formula to find the density of the brass specimen in \(\mathrm{kg/m^{3}}\).