Aptitude - Volume and Surface Area - Discussion

I cannot understand this, please explain.

We have given l=15, b=12.
Area of ceiling + floor = Area of four wall,
2(l*b) = 2(12*h)+2(15*h),
( because opposites walls are of same area)
2(15*12)=2h(12+15),
h=180/27.

Thanks @Lokesh.

Thanks for all the given explanation of the answer.

Thank you all for the given explanation.

Easy to understand now with the help of given explanation, Thank you all.

This is for your kind information,

Floor Area = 15 x 12 = 180 m.
Ceiling Area = 15 x 12 = 180 m.

Now, Sum of Floor & Ceiling Area = 180 + 180 m = 360 m.

As given in question that,
(Sum of Floor & Ceiling Area = Sum of Wall Area).

360 = 2(Hall Length x Hall Height) + 2(Hall Width x Hall Height).
360 = 2(15 x Hall Height) + 2(12 x Hall Height).

Here I consider Hall Height = h.

360 = 30h + 24h,
360 = 54h,
h = 360/54,
h = 20/3.
So, Hall Height = 20/3.

As we know,
Volume of Box = Length x Width x Height.
Volume of Box = 15 x 12 x 20/3.
Volume of Box = 1200 Cubic meter.

I cannot understand this. Someone help me.

We know the cuboid surface area formula is 2(xy+yz+zx).
In this question it says; area of (floor+ceiling) is equal to 4 walls area.
So floor area is x*y,
So floor+ceiling = 2xy.
We know cuboid has 6 surface . 2 surface area is 2xy , then other 4 surface equation is; 2(xy+yz+zx) - 2xy = 2(yz+zx) or 2(y+x)z.

So we write it like,
2(y+x)z = 360 {because see above that 2 surface is equal of 4 walls say in question.}
and now u find the "z"
x=15 and y =12 are given in question.
and we know, the volume of cuboid formula = x * y * z.

So, the answer is 1200m^3.

In the given question, the ceiling and floor are both rectangles. So if we find the summation of their area, then the area will be: (l x b) + (l x b) which equals to 2 x (l x b).

Now coming to the second part, it's given the sum of area of walls, that implies the part of the cuboid except for the ceiling and floor part which can be written as: (surface area of cuboid) - (area of floor and ceiling part) i.e 2(lb + bh + lh) - 2(lb) which is equal to 2h(l + b).

Now equate both the parts and get h as explained in te solution part.