Question

The length of a hall with a flat roof is $20$ m and width is $16$ m. If the sum of the areas of the floor and roof is equal to the total area of the $4$ walls, then the ratio of the Numerical value of the height to the volume of the hall is ?

• A. $1:600$
• B. $1:200$
• C. $1:240$
• D. $1:320$

Answer 1

The correct option is D $1:320$

Let the height of the hall be ${}^{\prime }{h}^{\prime }$ m.

Area of floor $=l\times b=20\times 16=320m^2$

Area of root $=l\times b=20\times 16=320m^2$

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 $=l\times b\times h=20\times 16\times \frac{80}{9}=\frac{25600}{9}{m}^3$

Ratio of height to volume $=\frac{800/9}{25600/9}=\frac{80}{25600}=\frac{1}{320}$

$1:320$