Question

A hall is $15m$ long and $12m$ broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of the $4$ walls, what is the volume of the hall?

• A. $2200m^3$
• B. $1500m^3$
• C. $1620m^3$
• D. $1200m^3$

Answer 1

The correct option is D $1200m^3$

Area of floor + Area of ceiling =Area of four walls
$\Rightarrow lb+lb=2\times h\times (l+b),$ where l, b, h are the length breadth and height of the hall
$\Rightarrow lb=h\times (l+b)$
$\Rightarrow 15m\times 12m=h\times (15m+12m)$
$\Rightarrow h=\frac{15\times 12}{27}m=\frac{20}{3}m$
$\therefore$ Volume of the hall $=l\times b\times h=15m\times 12m\times \frac{20}{3}m=1200m^3$