Question

Mathematician Euler understood that it is possible to discover the number of edges in a solid with the number of faces and vertices. In this way, it was possible to understand the total volume of three-dimensional objects. In an area of Maria's house, a cube-shaped aquarium will be built, which will be installed in the courtyard of her house. However, Maria would like to know the total volume of this cube, to know how much water she will use. As data, we have: the aquarium will be 1 meter high, 50 cm long and 70 cm deep. Regarding the total volume of the cube, analyze the following sentences: I- The volume will be 0.35 m3, that is, 350 liters. II- The volume will be 35 m3, that is, 3,500 liters. III- The volume will be 0.35 m3, that is, 3,500 liters

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Answer to a math question Mathematician Euler understood that it is possible to discover the number of edges in a solid with the number of faces and vertices. In this way, it was possible to understand the total volume of three-dimensional objects. In an area of Maria's house, a cube-shaped aquarium will be built, which will be installed in the courtyard of her house. However, Maria would like to know the total volume of this cube, to know how much water she will use. As data, we have: the aquarium will be 1 meter high, 50 cm long and 70 cm deep. Regarding the total volume of the cube, analyze the following sentences: I- The volume will be 0.35 m3, that is, 350 liters. II- The volume will be 35 m3, that is, 3,500 liters. III- The volume will be 0.35 m3, that is, 3,500 liters

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Santino

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102 Answers

\text{Given: Height } = 1 \, \text{meter}, \, \text{Length } = 0.5 \, \text{meters}, \, \text{Depth } = 0.7 \, \text{meters}

### Calculation of Volume

The formula to calculate the volume of a rectangular prism is:

V = \text{Height} \times \text{Length} \times \text{Depth}

Substitute the given values:

V = 1 \, \text{meter} \times 0.5 \, \text{meters} \times 0.7 \, \text{meters}

V = 0.35 \, \text{cubic meters (m}^3)

Since 1 cubic meter equals 1,000 liters:

0.35 \, \text{m}^3 \times 1,000 \, \text{liters/m}^3 = 350 \, \text{liters}

### Analysis of Statements

I. The volume will be 0.35 m³, that is, 350 liters.
- **Correct**. The volume is 0.35 cubic meters, which is equivalent to 350 liters.

II. The volume will be 35 m³, that is, 3,500 liters.
- **Incorrect**. The correct volume is 0.35 cubic meters, not 35 cubic meters, and 35 cubic meters would convert to 35,000 liters.

III. The volume will be 0.35 m³, that is, 3,500 liters.
- **Incorrect**. The volume of 0.35 cubic meters is correct, but it equals 350 liters, not 3,500 liters.

### Conclusion

The only correct statement is:

I. The volume will be 0.35 m³, that is, 350 liters.

\textbf{Answer: } \text{Volume = 0.35 cubic meters or 350 liters}

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