# The length of a hall is 20m and width 16m . The sum of the area of the floor and the flate roof is equal to the sum of the area of the four walls . find the height and the volume of the hall .

solution : Let the height of the hall be $h$ m . Then ,

sum of the areas of four walls $= 2(l+b)h m^2=2(20+16)h m^2=72h m^2$

sum of the areas  of the floor and flat roof $= (20\times16+20\times16)m^2=640m^2$

It is given that the sum of the areas of four walls is equal to the sum of the areas of the floor and roof.

$\therefore$              $72h= 640\Rightarrow h=\frac{640}{72}m=8.88m$

So, height of the the hall =8.88 m

Volume of the hall $=20\times 16 \times\frac{80}{9}m^3=\frac{25600}{9}m^3=2844.4m^3$

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