Question

If the length of cuboid is 12m, breadth 9m and height is 8m then find the length of diagonal of cuboid.

Answer 1

Hint:Given length, breadth and height of cuboid, Using the formula \[\sqrt{{{l}^{2}}+{{b}^{2}}+{{h}^{2}}}\] where l is length ,b is breadth and h is height of cuboid, we get length of diagonal of cuboid.

Complete step-by-step answer:
In the question we are told about the length of cuboid which is 12m, breadth of cuboid which is 9m and height of cuboid which is 8m and we have to find the diagonal of the box.
Before proceeding let’s learn something about cuboid in maths.
A cuboid is a 3 – D shape. Cuboids have six faces which form convex polyhedra. Broad faces of cuboids can be any quadrilateral. More narrowly and rectangular cuboids are mode from 6 rectangles, which are placed at right angles. A cuboid that has all faces square is called a cube. The properties are: -
1) It has 12 edges.
2) It has 8 corners or vertices.
3) It has 6 faces.
The basic difference between a rectangle and a cuboid is that one cone is 2 – D shape and the other is 3 – D shape.
The formula for finding the longest diagonal is \[\sqrt{{{l}^{2}}+{{b}^{2}}+{{h}^{2}}}\], where l, b, h represents length, breadth and height of cuboid which is given as 12m, 9m and 8m respectively.
So, according to the formula the value of the diagonal is \[\sqrt{{{8}^{2}}+{{12}^{2}}+{{9}^{2}}}\], which is on calculation equals to \[\sqrt{289}\] or 17. Hence the value of diagonal is 17m.
The length of the diagonal is 17m.

Note: There are similar questions that can be made using the same concept like the dimensions of cuboidal boxes are given and we have to find the longest box that fits in, then in that case we have to find the diagonal of cuboid.