Question

The total surface area of the cuboid of length 6 m and breadth 5 m is 126 sq. m. Find its height.

Answer 1

Hint: Given the length and breadth of cuboid so assume the height of cuboid as h m. Now substitute the values of length, breadth and height values in the formula of total surface area of cuboid then we will get the height of cuboid as we already know the value of total surface area of cuboid.

Complete step-by-step answer:
Let the height of cuboid be h m
Given that the length of the cuboid is 6 m
The breadth of the cuboid is 5m
The total surface area of the cuboid is \[126{{m}^{2}}\]
We know that the formula for total surface area of cuboid is given by \[2\left( lb+bh+hl \right)\]where l represents length and b represents breadth and h represents height.
Now the substitute the values of l, b, h in the above formula then we will get
\[\Rightarrow 2(5\times 6+5\times h+6\times h)=126\]. . . . . . . . . . . . . . . . . . . . . . (1)
\[\Rightarrow 30+11h=63\]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)
\[\Rightarrow 11h=33\]
\[h=\dfrac{33}{11}=3m\]
So the height of the cuboid is \[h=3m\]

Note: The formula for total surface area of cuboid is given by \[2\left( lb+bh+hl \right)\]and the formula for lateral surface area of cuboid is given by \[2h\left( l+b \right)\]where l, b, h represents length, breadth and height respectively. The cuboid is three dimensional and the faces of the cuboid can be any quadrilateral.