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1800-102-2727A 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.
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.
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.
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.