Question

The length and breadth of a brick are 10cm and 8 cm respectively. It’s total surface area is 1060 \[c{m^2}\]. It’s height is.

Answer 1

Hint: Total surface area of a cuboid is\[ = 2(lb + bh + hl)\]where, l=length of the cuboid; b= breadth / width of the cuboid and h=height of the cuboid.

Complete step-by-step answer:

 Given, the length of the brick=10cm
  The breadth of the brick=8cm
Total surface area of the brick=1060\[c{m^2}\]
Using formula for total surface area
\[
   = 2(lb + bh + hl) = 1060 \\
   = 10 \times 8 + 8 \times h + h \times 10 = \dfrac{{1060}}{2} \\
   = 80 + 8h + 10h = 530 \\
   = 18h = 450 \\
   \Rightarrow h = 25 \\
\]
The required height of the brick is 25 cm.

Note: The total surface area (TSA) of the cuboid is the sum of the areas of its six faces. We must require three variables length (l), width/breadth (b) and height (h) of the cuboid to find the total surface area of the cuboid.