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Volume of a Cuboid - Definition, How to find the Diameter and Deriving the volume of a Cuboid

 

Definition

A cuboid is the three-dimensional version of a rectangle. Well, partially. It is a convex polyhedron (a convex shape with many finite points that are not in the same plane), with six quadrilateral faces, eight vertices, and twelve edges. The polyhedral graph of a cuboid is the same as that of a cube.

There are many types of cuboids, like rectangular hexahedron, right rectangular prism, right cuboid, rectangular parallelepiped, and rectangular cuboid.


Volume of cuboid
The space or cavity inside a cuboid is called its volume. 

The volume of a cuboid = l x b x h units3

where l = length of the cuboid 

b = breadth of the cuboid 

h = height of the cuboid 

That means we can fill lbh unit cubes of water inside a box of length l, breadth b, and height h.


Deriving the volume of a cube from the volume of a cuboid

We know that the volume of a cuboid is length multiplied by breadth multiplied by height. Imagine all the sides of a cuboid are the same. 

Then, l x b x h = a x a x a         (considering all the sides as length a) --------------------------- (1) 

Therefore, the volume of the cuboid = a3 = volume of the cube 

Hence, proved. 

Do you know? 

What is the most extensive length of a rod that can be inserted inside a cuboid? 

Hint: Use Pythagoras theorem. 

Answer: BH 

Fun activity: Let us find out how many cubes can fit inside a giant cuboid! 

Consider some cubes with side S. All the cubes are symmetric and identical in shape and size. Now, consider a cuboid with sides L, B, H. 

Volume of a cube = S x S x S 

Volume of a cuboid = LBH 

Number of cubes inside a cuboid = Volume of the smaller element / Volume of the more prominent element                                                        

= Volume of a cube / Volume of a cuboid                                                           

= S x S x S / LBH 

The number which we will get will be the number of cubes that can fit inside the cuboid.
 

How to find the diameter of the possible giant sphere inscribed in a cube or cuboid?

Volume of a cube = a3 ----------------------------------------------- (2) 

Where a is the side of a cube 

Volume of a sphere = 4/3 π r3 ------------------------------------------- (3) 

Where r is the radius of the sphere 

Equating (2) and (3), we can find the sphere radius that can fit inside a cube. 

Fun Fact: The size of this sphere will be 47.6% smaller than the size of the cube. How? Find out for yourself! 

Consider the minor side of the cuboid to calculate the size of a sphere. Also, many such spheres can be placed inside the cuboid because of its varying sides. 

 

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