Math Problem Statement
Solution
The image you uploaded contains a multiple-choice question in Russian. Here is a translation of the statements for clarity:
- The volume of a cube with a side length of 10 cm is equal to one cubic decimeter.
- The general formulas for the volume of a rectangular prism and a right cylinder are of the same form.
- The volume of a right parallelepiped is equal to the product of its three dimensions.
- In one cubic centimeter, there are 1000 cubic millimeters.
- The volumes of bodies are measured in cubic units.
- One liter is equal to one cubic centimeter.
Now, let’s analyze these statements one by one:
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Volume of a cube: The volume of a cube is given by , where is the side length. For a cube with a side length of 10 cm, the volume would be: Since , . Therefore, the statement is correct.
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Formulas for volume: The volume formulas for a rectangular prism and a right cylinder differ. The formula for the volume of a rectangular prism is , while for a cylinder, it is . Hence, the statement is incorrect.
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Volume of a parallelepiped: The volume of a right parallelepiped is indeed calculated as the product of its three dimensions. Therefore, the statement is correct.
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Cubic centimeters and millimeters: One cubic centimeter is equal to 1000 cubic millimeters because , so . Therefore, the statement is correct.
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Measurement of volumes: Volumes are indeed measured in cubic units (e.g., cubic centimeters, cubic meters). Therefore, the statement is correct.
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Liter and cubic centimeter: One liter is equivalent to 1000 cubic centimeters, not just one cubic centimeter. So, this statement is incorrect.
Thus, the correct statements are:
- Statement 1
- Statement 3
- Statement 4
- Statement 5
Would you like further details or explanations on any of these? Also, here are some related questions you might find interesting:
- How is the volume of a sphere calculated?
- What are the units of volume in the metric system?
- How do you convert cubic centimeters to liters?
- What is the formula for the volume of a cone?
- How do you find the volume of irregular shapes?
Tip: When working with volume conversions, always check if the units are consistent, such as converting cubic centimeters to liters by dividing by 1000.
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Math Problem Analysis
Mathematical Concepts
Volume of geometric solids
Units of volume
Cube volume
Parallelepiped volume
Cylinder volume
Formulas
Volume of a cube V = a^3
Volume of a rectangular prism V = l × w × h
Volume of a cylinder V = π r^2 h
Theorems
Volume of a cube
Volume of a parallelepiped
Conversion between cubic millimeters and cubic centimeters
Suitable Grade Level
Grades 6-9
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