What is the volume in L of a cube with an edge length of 7.0 dm?

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Identify the formula for the volume of a cube: \( V = a^3 \), where \( a \) is the edge length.

Convert the edge length from decimeters to meters if necessary. In this case, 7.0 dm is equivalent to 0.7 m.

Substitute the edge length into the volume formula: \( V = (7.0 \text{ dm})^3 \).

Calculate the cube of the edge length: \( 7.0^3 \).

The result will give you the volume in cubic decimeters (dm³), which is equivalent to liters (L) since 1 dm³ = 1 L.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Volume of a Cube

The volume of a cube is calculated using the formula V = a³, where 'a' is the length of one edge. This formula arises from the fact that a cube has equal dimensions in all three spatial directions, allowing for straightforward multiplication of the edge length by itself three times.

Unit Conversion

In this question, the edge length is given in decimeters (dm), and the volume needs to be expressed in liters (L). Understanding unit conversion is essential, as 1 dm³ is equivalent to 1 L. Therefore, converting the volume from cubic decimeters to liters requires recognizing this relationship.

Cubic Measurements

Cubic measurements refer to the volume of three-dimensional objects, typically expressed in cubic units. When calculating the volume of a cube, the result is in cubic decimeters (dm³) if the edge length is in decimeters. This concept is crucial for ensuring that the final volume is correctly interpreted in the desired unit of liters.