Question

A goldsmith was ordered to make a crown. He was given $1000\text{g}$ of gold to make this. The finished product weighed $1000\text{g}$ but only displaced a volume of $25\text{mL}$ when put in a measuring cylinder that contained water. What of the following might have happened? (density of pure gold = $19.3{\text{g cm}}^{-3}$)

• A. A lower density material is added to the gold in making the crown.
• B. The density of gold decreased.
• C. A higher density material is added to the gold in making the crown.
• D. None of the above

Answer 1

The correct option is A A lower density material is added to the gold in making the crown.

pure gold has a density of $19.3{\text{g cm}}^{-3}$
the volume of $1000\text{g}$ gold will be $\frac{1000}{19.3}=51.8{\text{cm}}^3$

It is given that volume of water displaced by crown is $25\text{mL}=25{\text{cm}}^3$
$\because 1\text{mL}=1{\text{cm}}^3$

The volume of the crown if made from pure gold will be $51.8{\text{cm}}^3$
The volume of the crown made by the goldsmith is $25{\text{cm}}^3$
but both the crowns have the same mass.
This is because a metal of lower density than gold was added to make up for the mass and thereby the volume of the crown was lesser than it should have originally been.