1. The arms of the balance scale are not the same length.

2. The Principle of Moments is expressed by w₁d₂ = w₂d₁. The weights of the objects are inversely proportional to the lengths of the arms of the scale.

3. Using x for the weight of the cone results in two equations:
   
   w₁d₂ = xd₁
   
   xd₂ = w₂d₁
   
   Multiplying left and right sides gives
   
   x²d₁d₂ = w₁w₂d₁d₂
   
   x =
   
4. The formula does not use the lengths of the arms of the balance scale. You could find the weight of the cone with a different scale-as long as the objects balanced as shown in the drawings.

Solution