Question

1. a cube has a volume of (2^3) cubic inches. select all statements that are true about the cube.

a. the volume of the cube is 8 cubic inches.
b. the edge length of the cube is 3 inches.
c. the expression (3 cdot 2) also represents its volume in cubic inches.
d. the edge length of the cube is 2 inches.
e. the volume of the cube is 6 cubic inches.

Explanation:

Step1: Recall the formula for the volume of a cube

The volume \( V \) of a cube with edge length \( s \) is given by \( V = s^3 \).

Step2: Analyze each option

• Option A: Calculate the volume when \( s = 2 \). Using the formula \( V = 2^3 = 8 \) cubic inches. So this statement is true.
• Option B: The edge length is given by the base of the exponent in the volume expression \( 2^3 \). Here, the edge length \( s = 2 \), not 3. So this statement is false.
• Option C: The expression \( 3\cdot2 = 6 \), but the volume is \( 2^3 = 8 \), not 6. So this statement is false.
• Option D: From the volume formula \( V = s^3 = 2^3 \), we can see that the edge length \( s = 2 \) inches. So this statement is true.
• Option E: The volume of the cube is \( 2^3 = 8 \) cubic inches, not 6. So this statement is false.

Answer:

A. The volume of the cube is 8 cubic inches, D. The edge length of the cube is 2 inches