Question

A hall is 15m long and 12m broad.if the sum of the areas of the floor and the ceiling is equal to the sum of areas of the four walls the volume of hall is?

Answer 1

Given :

• Length of the hall = 15 m.

• Breadth of the hall = 12 m.

• The sum of the areas of the floor and the ceiling is equal to the sum of areas of the four walls.

To find :

• Volume of the hall =?

Step-by-step explanation :

Length of the hall = 15 m.

Breadth of the hall = 12 m.

Firstly we have to find the Area Ceiling,

So,

We know that,

Area of Rectangle = Area of Ceiling = Length x breadth.

Substituting the values in the above formula, we get,

= 15 x 12

= 180.

Therefore, Area of the Ceiling = 180 m².

Now,

Area of Rectangle = Area of Floor = Length x breadth.

Substituting the values in the above formula, we get,

= 15 x 12

= 180.

Therefore, Area of the floor = 180 m².

Now,

Total Area = Area of Ceiling + Area of Floor

Substituting the values, we get,

= 180 m² + 180 m²

= 360 m²

Therefore, Total Area = 360 m². ..... (i)

Now,

We have to find Area of four walls,

So,

Area of four walls = 2( h × b + h × l )

Substituting the values in the above formula, we get,

= 2 ( h x 12 + h x 15)

= 2 ( 12h + 15h)

= 2 × 27h

Therefore, Area of four wall = 2 × 27h. ㅤㅤ.... (ii)

It is Given that :

The sum of the areas of the floor and the ceiling is equal to the sum of areas of the four walls.

So,

Equation (i) and (ii) are equal,

2 x 27h = 360 m²

h = 360/2 x 27

h = 20/3 m.

So, The volume of the hall will be,

Volume of hall = Length × Height × Breadth

Substituting the values in the above formula, we get,

= 12 x 15 x 20/3

= 12 x 5 x 20

= 1200.

Therefore, Volume of the hall = 1200 m³.

Answer 2

Answer:

Given information –

• Length of the hall is 15 m.
• Breath of the hall is 12 m.
• Also, sum of areas of floor and ceiling = sum of areas of four wall.

To Find –

• Volume of the hall.

Solution –

Now, let's find the area of floor.

As the dimension for the floor and the ceiling will be same.

We can say that, area of floor = area of ceiling.

So, length * breath.

➸ 15 * 12

➸ 180 cm²

Hence, sum of areas of floor and ceiling :

➸ 2*180 cm²

➸ 360 cm²

Now, the lateral surface area of the hall that is the area of all the four walls is :

➸ 2 (bh + hl)

➸ 2 (12*h + h*15)

➸ 2 (12h + 15h)

➸ (2 * 27h) cm²

According to the question,

➸ 360 cm² = (2 * 27h) cm²

➸ 27 = 360/2

➸ 27h = 180

➸ h = 180/27

➸ h = 6.66 cm

Volume of the hall = lbh

➸ Volume = 15*12*6.66

➸ Volume = 15*79.92

➸ Volume = 1,198.8 cm³