Math Problem Statement

Выберите верные утверждения: 1. Объём куба с ребром 10 см равен одному кубическому дециметру. 2. Общие формулы объёма прямой призмы и прямого цилиндра имеют одинаковый вид. 3. Объём прямого параллелепипеда равен произведению трёх его измерений. 4. В одном кубическом сантиметре 1000 кубических миллиметров. 5. Объёмы тел измеряются в кубических единицах. 6. 1 литр это кубический сантиметр.

Solution

The image you uploaded contains a multiple-choice question in Russian. Here is a translation of the statements for clarity:

  1. The volume of a cube with a side length of 10 cm is equal to one cubic decimeter.
  2. The general formulas for the volume of a rectangular prism and a right cylinder are of the same form.
  3. The volume of a right parallelepiped is equal to the product of its three dimensions.
  4. In one cubic centimeter, there are 1000 cubic millimeters.
  5. The volumes of bodies are measured in cubic units.
  6. One liter is equal to one cubic centimeter.

Now, let’s analyze these statements one by one:

  1. Volume of a cube: The volume of a cube is given by V=a3V = a^3, where aa is the side length. For a cube with a side length of 10 cm, the volume would be: V=103=1000cm3V = 10^3 = 1000 \, \text{cm}^3 Since 1dm=10cm1 \, \text{dm} = 10 \, \text{cm}, 1dm3=1000cm31 \, \text{dm}^3 = 1000 \, \text{cm}^3. Therefore, the statement is correct.

  2. 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 V=l×w×hV = l \times w \times h, while for a cylinder, it is V=πr2hV = \pi r^2 h. Hence, the statement is incorrect.

  3. 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.

  4. Cubic centimeters and millimeters: One cubic centimeter is equal to 1000 cubic millimeters because 1cm=10mm1 \, \text{cm} = 10 \, \text{mm}, so 1cm3=103mm3=1000mm31 \, \text{cm}^3 = 10^3 \, \text{mm}^3 = 1000 \, \text{mm}^3. Therefore, the statement is correct.

  5. Measurement of volumes: Volumes are indeed measured in cubic units (e.g., cubic centimeters, cubic meters). Therefore, the statement is correct.

  6. 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:

  1. How is the volume of a sphere calculated?
  2. What are the units of volume in the metric system?
  3. How do you convert cubic centimeters to liters?
  4. What is the formula for the volume of a cone?
  5. 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