# Measurement Formulas

Measurement formulas are the estimation of ratios of quantity it compares a quantity with a standard unit. The basic measurements are mass, distance, area, and volume. The measurement formulas help us find these basic measurements with the given parameters. They also include some conversion formulas like conversion of an inch to feet, meter to miles, etc. A few of the measurement formulas are given below along with a few solved examples.

## What Are Measurement Formulas?

Measurement formulas for the different objects are different. Measurement formulas are very necessary for our calculations of the parameters that we want to know. With measurement in math, we mean calculating, the perimeter, area, volume. Measurement formulas vary according to the dimensions of an object. The dimensions of an object can be classified as 2-dimensional shapes or 3-dimensional shapes. Let us learn about few measurement formulas based on the shapes.

### List of Measurement Formulas for 2-D Shapes

For 2-dimensional shapes, we can only measure length, area, and perimeter. Given below is a detailed tabular list for you to understand the measurement formula.

Shape Name |
Perimeter |
Area |

Square | 4a | a^{2 } square units |

Rectangle | 2(a + b) | l × w square units |

Triangle | a + b + c | ½ Base × height square units |

Parallelogram | 2(a + b) | base × height = b × h square units |

Isosceles Trapezoid | a + b+ c+ d | ½ (a + b)h square units |

Rhombus | 4a | ½ \(d_1\) × \(d_2\) square units |

Circle | 2πr | π r^{2 } square units |

### List of Measurement Formulas for 3-D Shapes

For 3-dimensional shapes, we can measure length, surface area, and volume. Given below is a detailed tabular list for you to understand the measurement formula.

Shape |
Lateral (curved) Surface Area |
Total Surface Area |
Volume |

Cube | 4a^{2} |
6a^{2} |
a^{3 } |

Cuboid | 2h (l + b) | 2 (lb + bh + lh) | l × b × h |

Cone | πrl | πr(r + l) | (1/3)πr^{2}h |

Cylinder | 2πrh | 2πr(h + r) | πr^{2}h |

Sphere | - | 2πrh or 4πr^{2 }(If a diameter of sphere = 2r) |
(4/3)πr^{3} |

Hemisphere | 2 π r^{2} |
3 π r^{2} |
(2/3)πr^{3} |

Prism | base perimeter × height | (2 × Base Area) + Lateral surface area or (2 × Base Area) + (Base perimeter × height) | B × h |

Pyramid | (1/2) P × slant height | LSA + base area = (1/2) P × slant height + B | (1/3) (Bh) |

## Examples Using Measurement Formulas

**Example 1:** Noah measured the sides of the square to 12 inches, what would be the area of this square? Solve it by using measurement formulas.

**Solution:**

To find: The area of a square.

The sides of the square = 12 inches (given)

Using measurement formulas,

Area of a Square = (side)^{2}

Area of a Square = (12)^{2}

= 144 m^{2}

**Answer:** **The area of a square is 144 m ^{2}.**

**Example 2: **Calculate the area of a circle whose radius is 10 units using the measurement formulas.

Solution: To measure: area of a circle

given: radius of a circle = 10 units

Area of a circle = π r^{2 } square units

= π (10)^{2 } square units

= 314.2 square units.

**Answer: The area of a circle is 314.2 square units.**

**Example 3: Using measurement formula find the volume of a cuboid whose length is 10 units, breadth is 9 units, and height is 5 units**.

**Solution: **To find the volume of cuboid

Volume of cuboid = l b h cubic units

= 10 × 9 × 5

= 450

**Answer:** The volume of the cuboid is 450 cubic units.

## FAQ's on Measurement Formulas

### What Is the Measurement Formula of Cone?

There are three specific measurement formulas for cone listed below:

The lateral surface area of cone = πrl

The total surface area of cone = πr(r + l)

Volume of a cone = (1/3)πr^{2}h

### What Is the Measurement Formula of Sphere?

There are two specific measurement formulas for sphere listed below:

The surface area of sphere = 2πrh or 4πr^{2 }(If a diameter of sphere = 2r)

Volume of a sphere = (4/3)πr^{3}

### What Is the Measurement Formula of Cylinder?

There are three specific measurement formulas for cylinder listed below:

The lateral surface area of cylinder = 2πrh

The total surface area of cylinder = 2πr(r + h)

Volume of a cylinder = πr^{2}h

### What Is the Measurement Formula of Cuboid?

There are three specific measurement formulas for cuboid listed below:

The lateral surface area of cuboid = 2h (l+b)

The total surface area of cuboid = 2 (lb + bh + hl)

Volume of a cuboid = lbh

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