Aptitude - Volume and Surface Area - Discussion

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.

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.

To simplify it, we can separate the equation and calculate the surface area and ceiling area which is 2(15*12)=360 in total. Now as per question, it says that 4 walls have a total area of 360.

Now, we have to find the height of wall. So lets assume height is x.

So as per question, (15*x)+(12*x)+(15*x)+(12*x)=360. (Which is equal to floor + ceiling area)
if we will solve this equation, we will get the height of wall as 20/3.

Now we can find the are of hall by 20*15*20/3 which is equal to 1200.

@Erika,

Here four walls does not include the floor and the ceiling which is the top floor. Out of the four walls, sum of the areas of 2 walls which are opposite to each other is length* height+ length*height= 2*length*height.

Similarly, the sum of the areas of the 2 remaining two walls which are opposite to each other is breadth*height+breadth*height=2* breadth*height. So, the sum of areas of 4 walls= 2lh+2bh=2h (l+b). While calculating the area of a wall must consider the height of the wall.

According to the question,

Sum of areas of floor and the ceilings= 4 walls area sum
Floor area = ceiling area.
Floor area= 12 * 15 = 180.
Therefore 360 = 4 areas of walls.
Floor-length = wall length.
So height of the wall = (360/4)/15= 90/15 = 6m.
the volume of the hall is one type of cuboid.
Therefore volume of cuboid = length * breadth * height.
Volume = 15 * 12 * 6 = 1080 meter cube.

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

Sum of Floor & Ceiling Area = 180 + 180 m = 360 m
- now,in the question "f the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls." it means ,
360+360 = 720.

Please, help me to get it.

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.

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].

Roof + ceiling area = 4 side walls.

W.k.t area of rectangle l x b.

(12 x 15) + (12 x 15)= 12h + 15h + 12h + 15h.
2(12 x 15) = 2(12h + 15h).
2(12 x 15) = 2h(12+15).
2(12 x 15)
----------------- = h
2 x 27

Volume = LBH.
L=15 b=12 and h is 54.
Then, Volume= 1200.