Calculation of Weight of the Metal Piece

To calculate the weight of the solid rectangular metal piece, we need to determine its volume and then multiply it by the weight per unit volume of the metal.

Step 1: Determine the Volume
The volume of a rectangular solid can be calculated by multiplying its length, width, and height. In this case, the length is given as 3m, the width is given as 1.5m, and the thickness is given as 3cm.

Converting the thickness from centimeters to meters:
1 cm = 0.01 m
Therefore, the thickness is 3cm x 0.01m/cm = 0.03m

Now, we can calculate the volume:
Volume = Length x Width x Thickness
= 3m x 1.5m x 0.03m
= 0.135 cubic meters

Step 2: Determine the Weight per Unit Volume
The weight per unit volume or density of the metal is given as 7? (unknown value).

Step 3: Calculate the Weight
Weight = Volume x Density
= 0.135 cubic meters x 7? kg/cubic meter
= 0.945? kg

Explanation
To find the weight of the metal piece, we followed these steps:

1. We determined the volume of the metal piece by multiplying its length, width, and thickness.
2. We converted the thickness from centimeters to meters to ensure consistency in units.
3. We calculated the volume of the metal piece to be 0.135 cubic meters.
4. The weight per unit volume or density of the metal was given as 7? (unknown value).
5. Finally, we multiplied the volume by the density to find the weight of the metal piece, which came out to be 0.945? kg.

Note: The weight of the metal piece cannot be determined accurately without knowing the specific value of the density.