Surface area, volume, and density

The fundamental unit of length appears in other spatial quantities such as surface area and volume. Surface area describes how many square units it takes to completely cover a surface. For example, the top of a 3 m × 3 m board has a surface area of 9 m2. A 3 m cube has a surface area of 54 m2. A sphere with a diameter of 3 m has a surface area of only 28.3 m2, considerably less than a cube of the same dimension. All units of surface area are units of length squared, such as square inches (in2) and square kilometers (km2). Read the text aloud
How to calculate surface area and volume
Volume measures an amount of space in units of length cubed. Examples include cubic meters (m3), cubic centimeters (cm3), and cubic inches (in3). Volume is such an important concept that there are specific units for it, such as liters and gallons. Volume-specific units can always be related to the fundamental length units on which they are based. For example, one liter is defined as a volume of 1000 cm3 and one gallon is 3,780 cm3. For simple geometric shapes, the surface area and volume can be calculated by using formulas such as the examples in the diagram below. Read the text aloud
Volume and surface area of geometrical shapes
Which has more mass, a block of steel or a block of wood the same size? Both blocks have the same volume but the steel block has more mass. The steel block has more mass because the density of steel is higher than the density of wood. The density of an object measures the concentration of matter in the object’s volume. The units of density are units of mass divided by units of volume, such as kilograms per cubic meter (kg/m3). Air has a low density, typically about 1 kg/m3. Steel has a much higher density of around 7,800 kg/m3. Read the text aloud
The equation for calculating density is given by equation (2.2).
(2.2) ρ= m V
ρ  = density (kg/m3)
m  = mass (kg)
V  = volume (m3)
Read the text aloud Show The range of densities in the universe
A conical narwhal tusk is 2.0 m long and 4.0 cm wide at the base. What is the volume of the narwhal tusk?
  1. 0.000838 m3
  2. 0.00335 m3
  3. 0.00251 m3
  4. 0.0127 m3
  5. Show
This narwhal tusk has a mass of 1.6 kg. What is the density of narwhal tusk?
  1. 0.0251 kg/m3
  2. 2,980 kg/m3
  3. 1,900 kg/m3
  4. 0.00127 kg/m3

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