Question

Find the length of the diagonal of the cuboid whose dimensions are:
(i) 2, 3 and 4 cm
(ii) 3, 4 and 5 cm

Answer 1

Hint: Here we will substitute the given dimensions in the formula of the length of the diagonal of the cuboid. Then by simplifying the equation, we will get the lengths of the diagonal of the cuboid. A Cuboid is a three-dimensional shape with six flat surfaces, eight vertices or corners and twelve edges.
Formula used: Diagonal of the cuboid, \[d = \sqrt {{l^2} + {b^2} + {h^2}} \] where, \[l\] is the length of the cuboid, \[b\] is the breadth of the cuboid and \[h\] is the height of the cuboid.

Complete step by step solution:
We will first draw the diagram of a cuboid.

(i) The given dimensions of the cuboid are 2, 3 and 4 cm.
Now by using the formula of the length of the diagonal of the cuboid, we get length of the diagonal of the cuboid as:
\[d = \sqrt {{2^2} + {3^2} + {4^2}} \]
Applying the exponent on the terms, we get
\[ \Rightarrow d = \sqrt {4 + 9 + 16} = \sqrt {29} cm\]
Hence, the length of the diagonal of the cuboid whose dimensions are 2, 3 and 4 cm is equal to \[\sqrt {29} cm\].
(ii) The given dimensions of the cuboid are 3, 4 and 5 cm.
Now by using the formula of the length of the diagonal of the cuboid, we get length of the diagonal of the cuboid as:
\[d = \sqrt {{3^2} + {4^2} + {5^2}} \]
Applying the exponent on the terms, we get
\[ \Rightarrow d = \sqrt {9 + 16 + 25} = \sqrt {50} cm\].

Hence, the length of the diagonal of the cuboid whose dimensions are 2, 3 and 4 cm is equal to \[\sqrt {50} cm\].

Note:
We should not get confused between cube and cuboid. We know that the faces of a cuboid are parallel to each other. Unlike cube, the sides of the cube are not equal. The length of all the edges of the cube is equal to each other but it does not happen in a cuboid. The Cube is the most symmetric in all hexahedron shaped objects. The diagonals of the cube are identical to each other but the diagonals of a cuboid are not equal.