Question

The length of a hall is 15m and width is 12m . The sum of the areas of the floor and flat root is equal to the sum of the areas of the four walls .The capacity of the hall is______.​

Answer 1

Answer:

The volume of the hall will be 1200 cubic metres.

Step-by-step explanation:

Let, the hight of the hall be, H metres.

Length of the hall, L=15 metres.

The breadth of hall, B=12 metres.

Sum of the area of floor and ceiling

=L*B+L*B

=2(L*B)

= 2*(15*12) sq.m

=360 sq.m

Sum of the area of four walls

=L*H+L*H+H*B+H*B

=2(L*H+H*B)

=2H(L+B)

=2H(15+12) sq.m

=2*27*H

=54H

Given, 54H=360

So, H= 203

So, The volume of the hall will be,

V=L*H*B

=15*12* 203 cubic metre

=1200 cubic metre

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Answer 2

Answer:

1200m

Step-by-step explanation:

First of all we need to know the basic formulas of Rectangle (because here the two sides are different, so definitely it will not be a Square)

Area of Rectangle = l*b

Volume of rectangular prism = l*b*h

Note:

Square(2- dimension) = Cube(3-dimention)

Rectangle (2-dimension) = Rectangular Prism(3- dimension)

In the given question, L = 15, B = 12

So, Area = l*b = 15*12 = 180 m²

Now, here we had calculated the area for Floor of the Hall & we know that area of both Floor and Ceiling in a hall will be equal, which means

Area of Floor = Area of Ceiling = 180m²

Hence, Sum of their area = 180+180 = 360m²

In the question, also they had mentioned that Sum of the area of Floor and Ceiling is equal to the sum of the area of four walls in a Hall.

Square = 4 sides are equal

Rectangle = only 2 opposite sides are equal

In case of 3-dimension,

If the hall is in Cube shape, the area of all the 4 walls will be equal. But, here we know that the hall is in Rectangular Prism shape, so only area of 2 opposite walls will be equal.

Area of two walls = 15*b + 15*b = 30b

Area of other two walls = 12*b + 12*b = 24b

Hence,

Their Sum = 30b + 24b = 54b

360 = 54b which means b = 360/54 = 20/3

Here, the breadth of the walls is equal to the height of the rectangular prism (Hall)

Hence,

Volume of Hall = l*b*h = 15*12*(20/3) = 1200 m³

Hope you guys understand my explanation!!!