Question: 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
- 2100
“A hall is 15 m long and 12 m broad”- is a topic that belongs to the GMAT Quantitative reasoning section of the GMAT exam. GMAT quant tests the students’ talents to employ analytical and logical reasoning to crack mathematical problems. The students must choose the proper option by solving it with mathematical calculations. The students must have a more suitable understanding of qualitative to solve GMAT Problem Solving questions. The calculative mathematical problems of the GMAT Quant topic in the problem-solving part should be interpreted with better mathematical skills. The candidates can improve their knowledge by practicing more questions from the book “GMAT Official Guide Quantitative Review”.
Solution and Explanation:
Approach Solution 1:
The problem statement informs that:
Given:
- A hall is 15 m long and 12 m broad.
- Sum of the floor and ceiling areas of the hall is equal to the sum of the areas of four walls.
Find Out:
- The volume of the hall
As per the formula of the volume of a rectangular hall:
Volume = Product of the length, breadth and height of the rectangular hall
= length* breadth* height
Let the height of the rectangular hall be h.
Area of the rectangular floor = length x breadth = 15*12 =180
Area of the ceiling of the hall = length x breadth = 15*12 =180
Therefore, the area of the floor and ceiling of the hall = 180 + 180 = 360
There exist two walls whose length is 15 m and two walls whose length is 12m.
Area of walls 15m long = 2* 15* h = 30h
Area of walls 12m long = 2* 12* h = 24h
Therefore, the area of the 4 walls of the hall = 30h + 24h = 54h
It is given that the area of floor + area of ceiling = Area of the four walls.
Therefore, 360 = 54h
=> h= 360/54 = 20/3 m
Therefore, the volume of the rectangular hall= 15* 12* 20/3 = 1200 cubic meters.
Correct Answer: (C)
Approach Solution 2:
The problem statement suggests that:
Given:
- A hall is 15 m long and 12 m broad.
- Sum of the floor and ceiling areas of the hall is equal to the sum of the areas of four walls.
Find Out:
- The volume of the hall
The floor and ceiling of the hall are identical, i.e. they have the same length and breadth.
Therefore, the sum of the floor and ceiling of the hall = 2 (15* 12)
Let the height of the hall be x
Therefore, the sum of the area of the four walls = 2 (12x) + 2 (15x) [since two walls with a width of 12m and two walls with a length of 15m]
2 (15* 12) = 2 (12x) + 2 (15x)
=> (15* 12) = 12x + 15x
=> (15* 12) = x (12 + 15)
=> (15* 12) = 27x
=> x = 15 * 12/27
Therefore, the volume of a rectangular hall = length x breadth x height
= 15* 12* x
= 15* 12(15 * 12/27) = 1200 cubic meters.
Correct Answer: (C)
Approach Solution 3:
The problem statement states that:
Given:
- A hall is 15 m long and 12 m broad.
- Sum of the areas of the floor and ceiling of the hall is equal to the sum of the areas of four walls.
Asked:
- Find out the volume of the hall.
It is given that the length (l) = 15m, breadth (b) = 12m
Let’s assume that the height of the hall is h
According to the question,
Sum of the areas of the floor and ceiling of the hall is equal to the sum of the areas of four walls.
Therefore, the area of the floor = l x b
Therefore, the area of the ceiling = l x b
Therefore, the area of the walls = 2 (l + b)h
Thus we can say,
l x b + l x b = 2 (l + b) x h
=> lb = lh + bh
=> 15 x 12 = 15h + 12h
=> 180 = 27h
=> h = 20/3
Therefore, Volume of the hall = l x b x h
= 15 x 12 x 20/3
= 1200
Hence the volume of the hall = 1200 cubic meters
Correct Answer: (C)
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