Question

a student is given a metal sphere about the size of a softball and asked to identify what type of metal it is made of. it has a radius of 5.00 cm and a mass of 5.915 kg.

is it aluminum, zinc, iron, silver, lead, or platinum?

○ iron
○ zinc
○ aluminum
○ platinum
○ silver
○ lead

Explanation:

Step1: Calculate the volume of the sphere

The formula for the volume of a sphere is \( V = \frac{4}{3}\pi r^3 \). The radius \( r = 5.00\space cm \).
\[

$$\begin{align*} V&=\frac{4}{3}\times\pi\times(5.00)^3\\ &=\frac{4}{3}\times\pi\times125\\ &\approx 523.6\space cm^3 \end{align*}$$

\]

Step2: Convert mass to grams

The mass \( m = 5.915\space kg = 5915\space g \) (since \( 1\space kg = 1000\space g \)).

Step3: Calculate the density

Density \(
ho=\frac{m}{V} \). Substituting the values of \( m \) and \( V \):
\[

ho=\frac{5915}{523.6}\approx 11.3\space g/cm^3
\]
The density of silver is approximately \( 10.5\space g/cm^3 \), lead is about \( 11.3\space g/cm^3 \), iron is about \( 7.87\space g/cm^3 \), zinc is about \( 7.14\space g/cm^3 \), aluminum is about \( 2.70\space g/cm^3 \), platinum is about \( 21.45\space g/cm^3 \). So the density matches lead.

Answer:

Lead