Aptitude - Volume and Surface Area - Discussion

Discussion Forum : Volume and Surface Area - General Questions (Q.No. 3)
3.
A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:
720
900
1200
1800
Answer: Option
Explanation:

2(15 + 12) x h = 2(15 x 12)

h = 180 m = 20 m.
27 3

Volume = 15 x 12 x 20 m3 = 1200 m3.
3

Video Explanation: https://youtu.be/V8EQ1YIaH74

Discussion:
74 comments Page 1 of 8.

Debasish Sethy said:   3 years ago
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.
(7)

Subash chander said:   4 years ago
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.
(6)

Surajbhan Singh said:   4 years ago
2*(l*h)+ 2*(b*h)= 2*(l*b).

4 walls area = floor area + ceiling area.
(2)

Bharath bhargav said:   1 year ago
The area of the cuboid 2(l+b)*h.
(1)

Subash said:   3 years ago
I am not getting this, Anyone help me to get it out.
(1)

Manoj said:   6 years ago
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.
(1)

YASH said:   4 years ago
The solution is wrong as it is said it is equal to the area of the 4 walls so, 4 should be multiplied.
(1)

Geet said:   6 years ago
I cannot understand this! Please, anyone explain it.

Lokesh said:   7 years ago
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.

Ramesh said:   7 years ago
Thank for your explanation. @Sonu.


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