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
$$\begin{gathered} =2(lb+bh+hl)=1060 \\ =10\times 8+8\times h+h\times 10={\displaystyle \frac{1060}{2}} \\ =80+8h+10h=530 \\ =18h=450 \\ \Rightarrow h=25 \end{gathered}$$
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.