The volume of the figure is 75 in3. If the dimensions are tripled, what will the new figure's volume be?Question 1Select

1. ### Break Down the Problem

To find the new volume of a figure when its dimensions are tripled, we need to understand the relationship between the dimensions of a shape and its volume.

2. ### Relevant Concepts

The volume $V$ of a three-dimensional object is proportional to the cube of its linear dimensions. If the dimensions are scaled by a factor $k$, the new volume $V'$ can be calculated using the formula: $V' = k^3 \times V$ where $V$ is the original volume.

3. ### Analysis and Detail

In this case, the original volume $V$ is 75 in³, and the scaling factor $k$ is 3 (since the dimensions are tripled).

$V' = 3^3 \times 75$ Calculating $3^3$: $3^3 = 27$ Now, substituting back into the volume formula: $V' = 27 \times 75$

Now calculate $27 \times 75$: $27 \times 75 = 2025$

4. ### Verify and Summarize

The calculations show that if the dimensions are tripled, the volume increases by a factor of 27. The final volume of the figure, when the dimensions are tripled, is calculated correctly.

Final Answer

The new figure's volume will be $2025 \, \text{in}^3$.