Q1.41 P - Chemistry: Molecular Nature Of Matter And Change

Question

A steel ball-bearing with a circumference of $32.5 mm$ weighs $4.20 g$.What is the density of the steel in g/cm³ (V of a sphere = $\frac{4}{3}\pi r^3$  ; circumference of a circle =$2\pi r$ )?

Step-by-Step Solution

Answer

Density of the given steel ball comes out to be  $7.241gc{m}^3$ after the calculation using the given data.

Step 1: Density and Volume Definition and Formula

Density is the amount or mass present per unit volume and volume is the space occupied. In the question we have been provided a steel ball and ball represents a sphere.

 

For a sphere volume is space occupied within the sphere and it is calculated using the formula, $\mathrm{V}=\frac{4}{3}\pi r^3$

And, $Density=\frac{Mass}{volume}$

Step 2: Calculating Volume of the Steel Ball (Sphere)

For calculating volume first, we need to find out the radius.

 

 As given,   $circumference of circle =2\pi r=32.5 mm$

Step 3: Calculating Density of Steel Ball

As discussed, 

$\begin{array}{rcl}Dencity& =& \frac{Mass }{Volume}\\ & =& \frac{4.20 g}{0.58 c{m}^3}\\ & =& 7.241 g/c{m}^3\end{array}$

Hence, the density of the given steel ball is $\begin{array}{rcl}& & 7.241 g/c{m}^3\end{array}$