What is the volume of cube B if cube A has a volume of 1 cubic inch and each side of cube B is 1 inch longer than cube A?

What is the volume of cube B if cube A has a volume of 1 cubic inch and each side of cube B is 1 inch longer than cube A?

• A. 2 times
• B. 3 times
• C. 4 times
• D. 8 times

Answer: (D)

To determine the volume of cube B, first, we need to establish the side length of both cubes. Since cube A has a volume of 1 cubic inch, we can find its side length by taking the cube root of the volume. The cube root of 1 cubic inch is 1 inch, meaning each side of cube A measures 1 inch. Next, we know that each side of cube B is 1 inch longer than that of cube A. Therefore, the side length of cube B is 1 inch + 1 inch, which equals 2 inches. The volume of a cube is calculated using the formula: \[ \text{Volume} = \text{side length}^3 \] Applying this formula to cube B, we find: \[ \text{Volume of cube B} = 2^3 = 2 \times 2 \times 2 = 8 \text{ cubic inches} \] To find how the volume of cube B compares to that of cube A, we divide the volume of cube B by the volume of cube A: \[ \text{Comparison} = \frac{8 \text{ cubic inches}}{1 \text{ cubic inch}} = 8 \]

To determine the volume of cube B, first, we need to establish the side length of both cubes. Since cube A has a volume of 1 cubic inch, we can find its side length by taking the cube root of the volume. The cube root of 1 cubic inch is 1 inch, meaning each side of cube A measures 1 inch.

Next, we know that each side of cube B is 1 inch longer than that of cube A. Therefore, the side length of cube B is 1 inch + 1 inch, which equals 2 inches.

The volume of a cube is calculated using the formula:

[ \text{Volume} = \text{side length}^3 ]

Applying this formula to cube B, we find:

[ \text{Volume of cube B} = 2^3 = 2 \times 2 \times 2 = 8 \text{ cubic inches} ]

To find how the volume of cube B compares to that of cube A, we divide the volume of cube B by the volume of cube A:

[ \text{Comparison} = \frac{8 \text{ cubic inches}}{1 \text{ cubic inch}} = 8 ]