Question

Ширина зала 8 2/5 метра,длина его в два с половиной раза больше ширины,а высота составляет 3/13 длины.Зная,что масса 1 м3 воздуха равнв примерно 1 3/10 кг,определите какую массу имеет воздух наполняющий зал С ПРИМЕРАМИ

Answer 1

8 2/5=8,4
8,4*2,5=21м длина зала
21*3/13=63/13 =4 11/13высота зала
8,4*21*4 11/13=111132/130 куб.м зал
111132/130*1 3/10=111132/130*13/10=55566/50=1111,32кг масса воздуха в зале

Answer 2

Problem Analysis

We are given the dimensions of a room: the width is 8 2/5 meters, the length is two and a half times the width, and the height is 3/13 times the length. We are also given that the mass of 1 cubic meter of air is approximately 1 3/10 kilograms. We need to determine the mass of the air filling the room.

Solution

To find the volume of the room, we need to multiply the width, length, and height. Let's calculate each of these dimensions step by step.

Step 1: Convert the width to an improper fraction: The width is given as 8 2/5 meters. To convert it to an improper fraction, we multiply the whole number (8) by the denominator (5) and add the numerator (2). Then we put the result over the denominator (5): 8 * 5 + 2 = 42/5 meters.

Step 2: Calculate the length: The length is two and a half times the width. To find the length, we multiply the width by 2.5: 42/5 * 2.5 = 105/5 = 21 meters.

Step 3: Calculate the height: The height is 3/13 times the length. To find the height, we multiply the length by 3/13: 21 * 3/13 = 63/13 meters.

Step 4: Calculate the volume of the room: To find the volume, we multiply the width, length, and height: 42/5 * 21 * 63/13 = 5292/5 = 1058.4 cubic meters.

Step 5: Calculate the mass of the air: We are given that the mass of 1 cubic meter of air is approximately 1 3/10 kilograms. To find the mass of the air filling the room, we multiply the volume of the room by the mass of 1 cubic meter of air: 1058.4 * 1 3/10 = 1058.4 * 13/10 = 1373.92 kilograms.

Therefore, the mass of the air filling the room is approximately 1373.92 kilograms.

Example Calculation

Let's take an example to illustrate the calculations:

Given: Width = 8 2/5 meters Length = 2.5 * Width Height = 3/13 * Length Mass of 1 cubic meter of air = 1 3/10 kilograms

Step 1: Convert the width to an improper fraction: Width = 8 2/5 meters = 42/5 meters

Step 2: Calculate the length: Length = 2.5 * Width = 2.5 * 42/5 = 105/5 = 21 meters

Step 3: Calculate the height: Height = 3/13 * Length = 3/13 * 21 = 63/13 meters

Step 4: Calculate the volume of the room: Volume = Width * Length * Height = 42/5 * 21 * 63/13 = 5292/5 = 1058.4 cubic meters

Step 5: Calculate the mass of the air: Mass of air = Volume * Mass of 1 cubic meter of air = 1058.4 * 1 3/10 = 1373.92 kilograms

Therefore, the mass of the air filling the room is approximately 1373.92 kilograms.

Conclusion

The mass of the air filling the room is approximately 1373.92 kilograms.

Answer 3

Problem Analysis

We are given the dimensions of a room: the width is 8 2/5 meters, the length is twice the width plus half the width, and the height is 3/13 times the length. We are also given that the mass of 1 cubic meter of air is approximately 1 3/10 kilograms. We need to determine the mass of the air filling the room.

Solution

To find the mass of the air filling the room, we need to calculate the volume of the room and then multiply it by the mass of 1 cubic meter of air.

Let's calculate the dimensions of the room step by step:

1. Width of the room: 8 2/5 meters. 2. Length of the room: Twice the width plus half the width. - Length = 2 * Width + 1/2 * Width - Length = 2 * 8 2/5 + 1/2 * 8 2/5 - Length = 16 4/5 + 4 1/5 - Length = 21 meters. 3. Height of the room: 3/13 times the length. - Height = 3/13 * Length - Height = 3/13 * 21 - Height = 4.846 meters.

Now that we have the dimensions of the room, we can calculate the volume:

Volume = Width * Length * Height Volume = 8 2/5 * 21 * 4.846

To simplify the calculation, let's convert the mixed numbers to improper fractions:

Volume = 42/5 * 21 * 4 846/1000 Volume = 42/5 * 21 * 4 846/1000 Volume = 42/5 * 21 * 4 846/1000 Volume = (42 * 21 * 4 846) / (5 * 1000) Volume = 42 * 21 * 4 846 / 5 000

Now, let's calculate the volume:

Volume = 42 * 21 * 4 846 / 5 000 Volume = 4 846 652 / 5 000 Volume ≈ 969.33 cubic meters.

Finally, we can calculate the mass of the air filling the room:

Mass = Volume * Mass of 1 cubic meter of air Mass ≈ 969.33 * 1 3/10

To simplify the calculation, let's convert the mixed number to an improper fraction:

Mass ≈ 969.33 * 13/10 Mass ≈ 12 603.29 / 10 Mass ≈ 1 260.33 kilograms.

Therefore, the mass of the air filling the room is approximately **1,260