What is the primary result of doubling the length of an object's linear dimension on its volume?

What is the primary result of doubling the length of an object's linear dimension on its volume?

• A. No change in volume
• B. Doubles the volume
• C. Increases volume by a factor of four
• D. Increases volume by a factor of eight

Answer: (D)

When the length of an object's linear dimension is doubled, the volume increases by a factor of eight because volume is a three-dimensional measurement. To understand this concept, consider the formula for the volume of a cube, which is calculated by cubing the length of one of its sides. If the original length of a side is represented as \( L \), the original volume \( V \) would be \( V = L^3 \). When the length is doubled, it becomes \( 2L \), and the new volume \( V' \) would be calculated as: \[ V' = (2L)^3 = 8L^3. \] Thus, the new volume is eight times the original volume. This principle applies to any three-dimensional object, not just cubes, which is why the correct choice is that the volume increases by a factor of eight when the linear dimensions are doubled.

When the length of an object's linear dimension is doubled, the volume increases by a factor of eight because volume is a three-dimensional measurement. To understand this concept, consider the formula for the volume of a cube, which is calculated by cubing the length of one of its sides.

If the original length of a side is represented as ( L ), the original volume ( V ) would be ( V = L^3 ). When the length is doubled, it becomes ( 2L ), and the new volume ( V' ) would be calculated as:

[ V' = (2L)^3 = 8L^3. ]

Thus, the new volume is eight times the original volume. This principle applies to any three-dimensional object, not just cubes, which is why the correct choice is that the volume increases by a factor of eight when the linear dimensions are doubled.