Final answer:
By converting the given block's dimensions to millimeters and calculating its volume, we can divide this volume by the volume of a 5mm cube to find that 1,600 5mm cubes can be made from the block.
Step-by-step explanation:
To determine how many 5mm lead cubes can be made from a 10cm x 5cm x 4cm block, first we must convert all measurements to the same unit. Here, we will convert centimeters to millimeters. A centimeter is equal to 10 millimeters, so the block's dimensions in millimeters are 100mm x 50mm x 40mm.
Now, to find the volume of the block, we multiply these dimensions:
100mm x 50mm x 40mm = 200,000 cubic millimeters.
Since each lead cube has a volume of 5mm x 5mm x 5mm, the volume of one cube is:
5mm x 5mm x 5mm = 125 cubic millimeters.
To find out how many cubes can be made, we divide the total volume of the block by the volume of one cube:
200,000 cubic millimeters / 125 cubic millimeters = 1,600.
Therefore, the answer is 1,600 lead cubes can be made from the given block, which corresponds to option c).