Aptitude - Volume and Surface Area - Discussion

Please anyone explain each and every step of the solution.

Main formula is : Area of 4 walls of a room = 2 (Length + Breadth) x Height. [step 4 to find height].
Area of four walls = (area of the base ) + (area of ceiling) [step 3].
Area of base is (l * b)[step 1].
Area of ceiling is (l * b)[step 2].
Volume = (l x b x h) cubic units [step 5].

I think there is no need to take 2 (l+b). But why we consider that? Can anybody explain.

Surface area of cuboid is 2 (lb + bh + hl).

But surface area of 4 walls doesnt includes areas of floor+ceiling. Thats why Total area of walls = 2 (lb + bh + bl) - 2 (lb) = 2 (hb + lh) = 2(b + l)h.

Imagine it as cuboid i.e it has different breadth and height also has length.
Given condition,

2(15h) = 2(15 * h) + 2(12 * h).
Solve this to get h.
lbh = v.

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.

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.

I cannot understand this. Someone help me.

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.

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