Answer to Question #88405 in Physics for Vero

Question

A block of metal is 5 cm by 7 cm by 9 cm and has a mass of 854 grams. Calculate the density of the block and give your best guess of what it is made of. Express the density in both g/cm3 and kg/m3.

Answer 1

Let's first find the volume of the block:

$$V = a \cdot b \cdot c = 5 cm \cdot 7 cm \cdot 9 cm = 315 cm^3.$$

Then, we can find the density of the block of metal from the formula:

$$\rho = \dfrac{m}{V} = \dfrac{854 g}{315 cm^3} = 2.71 \dfrac{g}{cm^3}.$$

Let's, also, convert $g/cm^3$ to $kg/m^3$:

$$\rho = 2.71 \dfrac{g}{cm^3} \cdot \dfrac{1 kg}{1000 g} \cdot \dfrac{(100 cm)^3}{1 m^3} = 2710 \dfrac{kg}{m^3}.$$

As we can see from the table [1], the metal is made of aluminum.

[1]. https://www.engineeringtoolbox.com/metal-alloys-densities-d_50.html

Answer:

$\rho = 2.71 \dfrac{g}{cm^3} = 2710 \dfrac{kg}{m^3}.$