A rectangular metal block with a mass of 18 kg has dimensions of 0.1 m x 0.15 m x 0.2 m. Calculate the volume of the block and determine its density.

Answer: To calculate the volume of the rectangular metal block, we use the formula for the volume of a rectangle which is:

Volume = length × width × height

Given the dimensions of the block are 0.1 m x 0.15 m x 0.2 m, we plug these numbers into the formula:

Volume = 0.1 m × 0.15 m × 0.2 m = 0.003 cubic meters (m³)

To determine the density of the block, we use the formula for density:

Density = mass/volume

We have the mass of the block as 18 kg and the volume we just calculated as 0.003 m³, so the density would be:

Density = 18 kg / 0.003 m³ = 6000 kg/m³

So, the density of the metal block is 6000 kg per cubic meter.

Extra: Volume is a measure of how much three-dimensional space an object occupies. The units of volume are typically cubic meters (m³), cubic centimeters (cm³), liters (L), etc. For a rectangular block, calculating volume is simply a matter of measuring the length, width, and height and multiplying them together.

Density is a physical property of a substance that relates its mass to its volume. It's a measure of how much mass is contained in a given volume of the object. The units for density could be kilograms per cubic meter (kg/m³), grams per cubic centimeter (g/cm³), or pounds per cubic inch (lb/in³) among others. An object that is denser means it has more mass packed into a smaller volume. Understanding density is important because it affects whether objects will float or sink when placed in a fluid; less dense objects will float on more dense fluids.