## How to Calculate volume of an objectIn this tutorial, we will briefly learn the steps to calculate the volume of different objects. Before we move further, let us understand the definition of a volume. ## What is volume?The volume of a shape is the measure of how much 3-D (three-dimensional) space any object occupies. OR Volume is also defined by the capacity of water (or air, or sand, etc.,) that a shape could hold. As per the International System of Units (SI), if any object has its dimensions in meters, the standard volume will be cubic meters or m3. Volume is also measured in three different units, i.e., cubic centimeters or cm3, cubic inches or in3, and cubic feet or ft3. Different objects hold different volumes. We have learned about different solid shapes in three-dimensional geometry, including cube, cuboid, pyramid, sphere, cylinder, cone, etc. Let us discover the step-by-step formula to calculate the volume for all these 3-D geometry shapes: ## 1. Calculating the Volume of a CubeA cube is defined as ## Note: The cube has all identical sides of equal length, so without any second thought, you can pick any side to measure. If at any point you are sceptical and want to check whether the solid shape is a cube or not, measure each side of the object and determine if they are equal or not.## Formula
Volume Formula Used for Cube => side ^{3} => side * side * side
The volume of a cube can also be determined if you know the length of its diagonal. Volume Formula Used for Cube => √3 × d ^{3}/9Where d represents the 'diagonal of the cube'
## Examples
Volume = (side) = (6 cm) = 216 cm
Volume = √3 × d = √3 × (3√3 cm) = √3 ×(3√3 × 3√3 × 3√3)/ 9 = √3 × 81√3 / 9 = (√3 × √3) × 81 / 9 = 3 x 81 / 9 = 243 / 9 = 27 cm ## 2. Calculating the Volume of a CuboidA cuboid is defined ## Note: A cube is said as a special rectangular cuboid wherein all the rectangles faces are equal.## FormulaVolume Formula Used for Cuboid => length x width x height=> l x b x h
## Example
Solution: Capacity of cuboid tank = capacity of the cuboid tank Volume of cuboid = length × width × height = 15cm × 8cm × 9cm = 1080 cm Therefore, the cuboidal tank has a capacity of 1080 cm ## 3. Calculating the Volume of a CylinderA cylinder is defined ## FormulaVolume Formula of Cylinder: V = πr ^{2}hWhere 'V' represents the Volume of cylinder 'r' represents radius of the circular cylindrical base 'h' represents the height 'π' represents the constant pi (22/7 or round pi to 3.14)
To calculate the volume of a cylinder one must know its height and radius (the distance between the edge of the circle and its center point) of one of the flat ends. ## Example:
Solution: As per the formula, we know Volume of a cylindrical = πr Where r= 7m and h = 21m Putting the values of r and h in our formula Volume = 3.14 x 7 = 3.14 x 7 x 7 x 21 = 3231.06 m ## 4. Volume of a Regular Square PyramidA ## Formula:Volume of a regular pyramid = 1/3b ^{2}h,Where 'b' represents the of the regular the pyramid (the polygon at the bottom) 'h' represents the height of the pyramid (vertical distance from the base to top). ## Example
Then, the volume of the right square pyramid is V = 1/3 × b ⇒ V = 1/3 × 5 The volume of the right square pyramid is ;83.34 cm ## 5. Calculate volume of SphereThe sphere is ## FormulaVolume of Sphere (V): 4/3πR where 'V' represents the Volume of sphere 'r' represents radius of the sphere fixed distance 'π' represents the constant pi (22/7 or round pi to 3.14) ## Examples
Volume of a sphere = 4/3 πr where r= 6cm putting the value of r in our formula V = 4/3 x 3.14 x 6 V = 4/3 x 3.14 x 6 x 6 x 6 V = 904.32 cm
So, radius = diameter/2 = 8/2 = 4 cm As per the formula, the volume of sphere is; Volume = 4/3 πr V = 4/3 π 4 V = 4/3 x 3.14 x 4 x 4 x 4 V = 4/3 x 3.14 x 64 V = 267.94 cm ## Measuring the volume of irregular solidsIn the above part, we discovered how to calculate the volume of solid objects, but what about objects of irregular shape as shown in the below image. For regular 3-D figures, one can easily find their respective volume by measuring their dimensions and using the suitable volume formula. However, if you want to calculate the volume of an irregular shape, you need to apply the Archimedes formula.
## Conclusion:From the above observation, Archimedes concluded that the volume of water displaced in any container is equal to the volume of the object immersed in it. So, if you want to calculate the volume of an irregular object, follow the below-given steps that are based on Archimedes principle: - Take a
**container**(beaker, bucket, measuring cup or graduated cylinder) and**an irregular object for which you want to calculate the volume**. Ensure that the container's size should be bigger than the object so it can be submerged easily, and the container should have a scale. - The next step is to
**pour water into the container and measure the volume**with the help of its scale. - After that, immerse your irregular object inside the container. Make sure it
**should be entirely dipped inside the water to get the accurate volume**. The water level will rise, read off the measurements.
## Note: Archimedes principle will not work if your irregular object dissolves in water.- The above scale measurements are essential for
**determining the buoyancy force built on Archimedes' principle**. - Calculate the volume of the container before and after immersing the irregular stone in it.
**The difference between both the container volumes will be the actual volume of our irregular object.**
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