The length of a hall is `20\ m` and width `16\ mdot` The sum of the area of the floor and the flat roof is equal to the sum of the areas of the four walls. Find the height and the volume of the hall.

Explanation

Let the height of the hall be `h` m
Area of floor`=lxx b=20xx 16=320 m ^ 2`
Area of root `=lxxb=20xx16=320 m ^ 2`
Sum of areas of four walls `=2( l+b) h=2(20+16 ) h=72h m ^ 2`
Now, `72h=( 320+320) =640`
`h=frac { 640 }{ 72 } =frac { 80 }{ 9 } m`
Volume of hall `=lbh=20xx 16xx frac { 80 }{ 9 } =frac { 25600 }{ 9 } m ^ 3`
Ratio of height to volume `=frac { 800/9 }{ 25600/9 } =frac { 80 }{ 25600 } =frac { 1 }{ 320 }`
`1:320`