Question

Two cubes are described below.

a red cube has side lengths of 4 inches
a blue cube has side lengths that are 1 inch longer than those of the red cube
The formula V=s3 can be used to find the volume of a cube. What is the difference between the volume of the red cube and the blue cube?

A.
37 in3


B.
189 in3


C.
125 in3


D.
61 in3

Answer 1

To find the difference between the volumes of the red and blue cubes, we first need to calculate the volume of each cube using the formula \( V = s^3 \), where \( s \) is the side length of the cube.

1. **Calculate the volume of the red cube:**
- Side length of the red cube = 4 inches
\[
V_{\text{red}} = 4^3 = 4 \times 4 \times 4 = 64 \text{ in}^3
\]

2. **Calculate the side length of the blue cube:**
- The blue cube has side lengths that are 1 inch longer than those of the red cube.
- Side length of the blue cube = 4 inches + 1 inch = 5 inches

3. **Calculate the volume of the blue cube:**
\[
V_{\text{blue}} = 5^3 = 5 \times 5 \times 5 = 125 \text{ in}^3
\]

4. **Calculate the difference between the volumes:**
\[
\text{Difference} = V_{\text{blue}} - V_{\text{red}} = 125 \text{ in}^3 - 64 \text{ in}^3 = 61 \text{ in}^3
\]

So, the difference between the volume of the red cube and the blue cube is:

**D. 61 in³**