Calculate Total Building Volume: Sum of 16 Rooms with 3 Different Dimensions

To solve this problem, we'll follow these steps:

• Step 1: Calculate the volume for each type of room.
• Step 2: Multiply the volume by the number of respective rooms.
• Step 3: Sum these volumes to determine the building's total volume.

Let's proceed with the calculations:

Step 1: Calculate the volume for each type of room.
For the first type of room:

$V_1 = 4 \times 7 \times 3 = 84 \, \text{m}^3$

For the second type of room:

$V_2 = 9 \times 4 \times 7 = 252 \, \text{m}^3$

For the third type of room:

$V_3 = 11 \times 3 \times 12 = 396 \, \text{m}^3$

Step 2: Multiply each volume by the number of corresponding rooms.

Total volume for the first type of room:

$3 \times 84 = 252 \, \text{m}^3$

Total volume for the second type of room:

$7 \times 252 = 1764 \, \text{m}^3$

Total volume for the third type of room:

$6 \times 396 = 2376 \, \text{m}^3$

Step 3: Sum these results to find the total volume.

Total volume of the building:

$252 + 1764 + 2376 = 4392 \, \text{m}^3$

This means the total volume of the building is $4392 \, \text{m}^3$.