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The term "measurement" refers to the act of measuring something. Measurement activities are frequently carried out by students in school. Measurement activities are used to find out how much something weighs. It is the assessment of a specific quantity's ratios. It is calculated by comparing a given quantity to a standard unit. These are used to calculate the size, length, area, perimeter, volume, or amount of an object. The use of diverse formulations is strongly reliant on such activities. Distance, area, surface area, volume, circumference, density, mass, and other quantities are calculated using measurement formulas. Conversions of an inch to feet, kilometre to miles, and so on are something we do often.
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Measurement Formulas
Measurement formulas for various objects differ. For our calculations of the parameters, measurement formulas are essential. In physics, measurement refers to computing the perimeter, area, and volume. Measurement formulas differ depending on the object's dimensions. Mass, distance, area, and volume are the four basic measures. With the supplied characteristics, the measurement formulas assist us in locating these essential measurements. They also provide conversion formulas such as inches to feet, metres to miles, and so on. An object's dimensions can be classed as either 2-dimensional or 3-dimensional. To calculate the area of a rectangle, for example, we use the formula: A = L * B.
Measurement Formulas: Some Important Formulas
Some of the important measurement formulas are:
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Measurement Formulas: 2-D Shapes
We can only measure length, area, and perimeter of 2-dimensional shapes. As the name implies, 2D shapes are made up of only two of these measurements. A two-dimensional form has no depth. Because 2-D objects have two dimensions, we may measure them in one of two ways: we can compute the area they occupy or the perimeter (that is, the length of their boundary).
A complete tabular list is provided below to help you grasp the measuring formulas of 2D shapes:
| Name of the Shape | Measurement Formula |
|---|---|
| Circle | Perimeter = 2 π r Area = π r2 where r = radius of the circle |
| Isosceles Trapezoid | Perimeter = a + b + c + d Area = ½ (a + b)h square units where a, b, c, d are the sides of the isosceles trapezoid |
| Parallelogram | Perimeter = 2(a + b) Area = Base * Height where a and b are the length of two adjacent sides of parallelogram |
| Rectangle | Perimeter = 2(a + b) Area = Length × Width square units where a and b are the length of two adjacent sides of parallelogram |
| Rhombus | Perimeter = 4 a Area = ½ d1 × d2 square units where a = side of the rhombus d1, d2 = diagonals of the rhombus |
| Square | Perimeter = 4 a Area = a2 square units where a = side of the square |
| Triangle | Perimeter = a + b + c Area = ½ Base × height square units where a, b, c are the sides of the triangle |
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Measurement Formulas: 3-D Shapes
We can measure length, surface area, and volume of 3-dimensional shapes. A complete tabular list is provided below to help you grasp the measuring formula of 3D shapes:
| Shape | Lateral (curved) Surface Area | Total Surface Area | Volume |
|---|---|---|---|
| Cube | 4a2 | 6a2 | a3 |
| Cuboid | 2h (l + b) | 2 (lb + bh + lh) | l × b × h |
| Cone | πrl | πr(r + l) | (1/3)πr2h |
| Cylinder | 2πrh | 2πr(h + r) | πr2h |
| Sphere | - | 2πrh or 4πr2 (If a diameter of sphere = 2r) | (4/3)πr3 |
| Hemisphere | 2 π r2 | 3 π r2 | (2/3)πr3 |
| 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) |
Application of Measurement Formulas
To measure something, measurement formulas are used. It's a rough approximation of quantity ratios.
- Comparing a quantity to a standard unit is how measurement is done.
- They are used to calculate the size, length, or quantity of something.
- Area, surface area, volume, circumference, distance, and other measurements are determined using measurement formulas.
- They also account for conversion formulas such as inches to feet, metres to miles, and so on.
Measurement Formulas Solved Examples
Ques: Find the volume of a cuboid with a length of 10 units, a width of 9 units, and a height of 5 units using the measurement formula. (3 marks)
Ans: To find the volume of cuboid:-
Volume of cuboid = l b h cubic units
= 10 × 9 × 5
= 450 cubic units.
Ques: What would the area of this square be if Noah measured the sides to be 12 inches? Use measuring formulas to solve the problem. (3 marks)
Ans: The sides of the square = 12 inches (given)
Using measurement formulas, Area of a Square = (side)2
Area of a Square = (12)2
= 144 m2
Ques: What is the area of a triangle with a 5 unit base and a 9 unit height? (3 marks)
Ans: Base = 5 units
Height = 9 units
Area of a Triangle = base ∗ height
= 4×9
= 452
= 3√5 (6.7)sq.units
Ques: Using the measuring formulas, calculate the area of a circle with a radius of 10 units. (3 marks)
Ans: Given radius of a circle = 10 units
Area of a circle = π r2 square units
= π (10)2 square units
= 314.2 square units.
Ques: A rectangular park's measurements are 12 yards by 5 yards. Determine its area. (3 marks)
Ans: The area of a rectangle is the product of its length and width.
Thus, Area = 12×5
= 60 yard2
Ques: Assume a square with a side of 6 cm. Calculate the area, perimeter, and diagonal length. (3 marks)
Ans: Given, side of the square, s = 6 cm
Area of the square = s2 = 62 = 36 cm2
Perimeter of the square = 4 × s = 4 × 6 cm = 24cm
Length of the diagonal of square = s√2 = 6 × 1.414 = 8.484
Ques: A pond's length, width, and depth are 20.5 metres, 16 metres, and 8 metres, respectively. Calculate the pond's capacity in litres. (5 marks)
Ans: l = 20.5 m, w = 16 m, h = 8 m
Capacity of pond = l x w x h
= 20.5(16)(8) = 2624 m3
1 m3 = 1000 liters,
= 2624(1000) liters
= 2624000 liters
Things to Remember
- Measurement activities are performed to determine the weight of something. It is determined by comparing a given quantity to a reference unit.
- Measurement formulas are used to compute distance, area, surface area, volume, circumference, density, mass, and other values.
- A two-dimensional shape has length and width but no depth, whereas a three-dimensional shape is a solid figure, an object, or a shape with three dimensions — length, width, and height.
- Measurement formulas are used to calculate area, surface area, volume, circumference, distance, and other dimensions.
- The formulas for measuring various objects differ. Measurement formulas are necessary for our computations of the parameters we want to know.
Frequently Asked Questions
Ques: What Is the Cylinder Measurement Formula? (3 marks)
Ans: The following are three different cylinder measuring formulas:
- 2πrh is the lateral surface area of a cylinder.
- The cylinder's total surface area is 2rπ(r + h).
- πr2h is the volume of a cylinder.
Ques: What is the definition of time measurement? (2 marks)
Ans: The order in which events occur is referred to as time. It is used to keep track of how long things take. It also allows us to specify the start and finish times of the events.
Ques: What is the square metre calculation formula? (3 marks)
Ans: Multiply the height in metres by the width in metres to get the square meterage of a rectangular rectangle. The resulting number shows the total number of square metres of geometric space contained in a given area. This is a calculation of a multi-dimensional area.
Ques: What is the formula for calculating cone measurement? (3 marks)
Ans: The following are three measuring formulas for cone:
- The cone's lateral surface area = πrl
- πr(r + l) is the total surface area of a cone.
- (1/3)πr2h is the volume of a cone
Ques: How do you calculate the volume of solid shapes? (3 marks)
Ans: The space occupied or delimited by any 3-D object or solid shape is referred to as volume. When the object is placed inside the can, the volume of liquid in the can is 15 units, and the volume of water is 50 units.
As a result, the object's volume is 50 – 15 = 35 units.
Knowing the volume of an object can help us figure out how much we'll need to fill it. Take, for example, the volume of water in a bottle.
Ques: What is the Cuboid's Measuring Formula? (3 marks)
Ans: The following are three different cuboid measurement formulas:
The cuboid's lateral surface area is 2h (l+b).
2 (lb + bh + hl) is the total surface area of a cuboid.
lbh is the volume of a cuboid.
Ques: What is the area of the surface? (1 mark)
Ans: A solid shape's surface area is the combined area of all of its faces. As a result, the surface area of a solid object with flat faces equals the sum of all of its faces.
Ques: What Is the Formula for Sphere Measurement? (2 marks)
Ans: The following are two specific sphere measuring formulas:
If the diameter of the sphere is 2r, the surface area of the sphere is 2rπh or 4πr2.
A sphere's volume is equal to (4/3)πr3.
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