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Mathematics

Difference between Area, Volume, and Surface Area

Difference between Area, Volume, and Surface Area

The volume of an object is the amount of space in a particular three-dimensional object. The area is the amount of space an object takes up in two dimensions. In contrast, the surface area of any solid object is the entire area that the object’s surface occupies (Sobecki, 2018). So, how can it be explained in class for learners to understand using different objects?

The area is the amount of space an object occupies in two dimensions. It can also be defined as the measure of the number of unit squares covering a closed object’s surface (Sobecki, 2018). The area is calculated using different formulas for various shapes. For instance, how can we find the area of the circle below?

Suppose the circle above has a radius of 14 cm. How can we find its area?

  • A= πr2 (π- 3.14)
  • A= 3.14×14×14
  • A= 615.44cm2

An object’s surface area is the measure of the complete area that an object’s surface takes up. It also has different formulas for various shapes, but this discussion will use a cuboid to calculate surface area.

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Surface Area of a cuboid=2× (Front+ side +Top)

Area of Front = L×W ×2

  • = 8cm×6cm×2 =96cm2

Area of side= L×W×2

  • =5cm×6cm×2= 60cm2

Area of Top= L×W×2

  • =8cm×5cm×2= 80cm2

Then add the three answers = 96 +60+80= 236cm2

Finally, volume is the quantity of space in a particular three-dimensional shape; it is calculated by simply multiplying a given object’s length, width, and height (Sobecki, 2018). Thus, the formula is Volume (V)=L×W×H.

For example, Jane holds a square cuboid with a width of 4cm, length of 4cm and a height of 4cm, as shown in the shape below. To calculate the volume of Jane’s cuboid, we multiply the length by the width by the height.

V= L×W×H

V=4cm×4cm×4cm = 64cm3

Therefore, this means Jane is holding a square cuboid whose volume is 64 cubic centimetres.

Reference

Sobecki, D. (2018). Math in Our World (2018) (4th ed., pp. 450-477). McGraw-Hill Education.

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Question 

Explain the difference between area, volume, and surface area.

Difference between Area, Volume, and Surface Area

Difference between Area, Volume, and Surface Area

Select a geometric shape and give an example of how to calculate its surface area and volume. How would you teach these concepts to a class?