Contents

### Key differences

The difference between area and volume is that area is the space covered by an object while the volume may be defined as space an object contains within itself. In other words, we can say that volume determines the capacity of an object whereas, area determines the space it occupies (two dimensional).

### Area vs. Volume

The area is space covered by an object whereas the volume is the capacity of an object. Area basically counts only two dimensions of an object. Whereas, the volume includes all the three major dimensions. When we talk about the area, it will give an objects outer occupied space whereas volume means the inner capacity an object can hold. For example, in case of rectangular box , when it comes to the area, we will only include two dimensions, width and length of the object whereas when it comes to volume, we may include all the three dimensions i.e. length, width and height. A point to remember here is that the formulas for the area and volume vary from figure to figure depending upon its shape.

### Comparison Chart

Basis | Area | Volume |

Definition | It is a region covered by an object. | It is the space occupied by an object. |

Dimensions | The area is two-dimensional calculations. | Volume is a three-dimensional calculation. |

Shape | Is a plain figure. | Is a solid object |

Unit | The area is calculated in the square term. For example ft^{2}, m^{2}, inch^{2} etc. | The volume is calculated in the cubic term. For example ft^{3}, m^{3}, inch^{3} etc. |

### What is the area?

The area is the two-dimensional measurement of an object. The area basically demonstrates the 2D part of an object covering the area. There are different methods to calculate the area for a different shape. In our daily lives, we calculate the area for several purposes. It goes from a carpet in a room to the car in a garage. We tend to calculate the area for the efficient settlement of our objects. If the area of a room is unknown, it is impossible to take a carpet that may fit in exactly. Apart from our daily lives the term area is also widely used in other fields either it is engineering or it is arts. The area is calculated for plain figures, unlike volume. Area helps to determine how many squares will fit in a particular solid figure. The System International (S.I) unit for area is meter per square, which is denoted as ‘m^{2}’. Calculation of area varies from shape to shape. Following are some formulas for calculation of some different shapes.

Shape | Area | Variable |

Square | A= L^{2} | Here L is the length of the side, i.e. all the sides of a square are equal. |

Rectangle | A=L×W | Here L is the length and W is the width of the rectangle |

Triangle (when base and height are known) | A= ½ B×H | Here B is the base and H is the height |

Triangle (when all three dimensions are known) | A=[s×(s-a)(s-b)(s-c) ]^{/2 }where S = (a+b+c)/2 | S is the semiperimeter of the triangle and a, b, and c denotes the side lengths of the triangle |

Circle | A=πr^{2} | Here π is the constant usually taken as(22/7 approximately = 3.14) and r is the radius of the circle |

Trapezoid | A= (b_{1}+b_{2})/2 × h | Here b_{1} and b_{2} is the length of the parallel sides and h is the distance between the two parallel sides. |

Parallelogram | A=b×h | Here b is the length of the base and h is the height. |

### What is volume?

Volume is the three-dimensional calculation of an object. It is the space with the three dimensions. In other words, the volume can also be called the capacity of the object. For example, the amount of water a bottle can hold is its volume. The system international unit for the volume is m^{3}. Alike area the formula for volume changes with the change in shape of the object. Following are some formulas for few shapes.

Shape | Volume | Variable |

Cube | V=S^{3} | Here S is the length of the side, i.e. all the sides of a cube are equal. |

Right Rectangular Prism | V=LWH | Here L is the length, W is the Width and H is the height of the right rectangle prism. |

Prism | V=AH | Here A is the base area (A is given in the table above), and H is the height. |

Pyramid or Cone | V=1/3 AH | Here A is the base area, and H is the height. |

Sphere | V=4/3 πr^{3} | Here π is the constant usually taken as (22/7 approximately = 3.14) and r is the radius of the sphere. |

### Key differences

- The space covered by a plane figure is known as an area whereas space covered by a three-dimensional object is known as the volume.
- The area is calculated for a two-dimensional figure while volume is calculated for the three-dimensional
- The area is the space that an object covers (2D) while volume is the capacity of an object.
- Solids have volume while plane figures only have area.
- The area is calculated in terms of square units while the volume is calculated in terms of cubic unit.
- The System International unit for area is m
^{2}while for volume is m^{3}.

### Conclusion

The discussion above clearly illustrates that the two mathematical terms area and volume are entirely different from each other. The area is a two dimensional, calculated for plane figures, measured in terms of square unit and varies from figure to figure. On the hand volume is a three dimensional, calculated for solid figures, measured in terms of cubic units, also known as the capacity of an object and varies from shape to shape.