Answer:The diagonal of a cuboid is 10√2 cm.
_______________________Given:
A cuboid with -
- Length = 10 cm
- Breadth = 8 cm
- Height = 6 cm
To Find:
Solution:
Let length, breadth and height be l, b and h respectively.
To find the diagonal we need to use,
[tex]\sf \implies Diagonal = \sqrt{l^2+b^2+h^2}[/tex]
Substituting the values,
[tex]\sf \implies Diagonal = \sqrt{(10)^2+(8)^2+(6)^2}[/tex]
Solving the equation,
[tex]\sf \implies Diagonal = \sqrt{100+64+36}[/tex]
[tex]\sf \implies Diagonal = \sqrt{200}[/tex]
[tex]\sf \implies Diagonal = \sqrt{100\times 2}[/tex]
[tex]\sf \implies Diagonal = 10\sqrt{2} \: cm[/tex]
More Formulae:
For cuboid -
Total Surface area = 2(lb + bh + lh )
Lateral Surface area = 2h(l + b)
Volume = (lbh)
Diagonal = √(l² + b² + h²)
Perimeter= 4(l + b + h)
For cube -
Total Surface Area = 6(a)²
Lateral Surface Area = 4(a)²
Volume of cube = (a)³
Diagonal of a cube = √3l
Perimeter of cube = 12a