Question

The area of a face of a cube can be found by evaluating the expression v^2/3, where v is the volume of the cube. What is the area of a face of a cube with a volume of 8 cm^3?

A. 8 cm^2
B. 4 cm^2
C. 16 cm^2
D. 64 cm^2

Answer 1

The area of a face of a cube with a volume of 8 cm³ is 4 cm².

Step-by-step explanation:

The question asks for the area of a face of a cube when given the volume of the cube. To find the area of a face of a cube with a volume of 8 cm³, we can use the given expression v²/3. Since the volume (v) is 8 cm³, we substitute this value into the expression to get (8 cm³)²/3. First, square the volume: (8 cm³)² = 64 cm¶. Then divide by 3: 64 cm¶/3 = 64/3 cm¶. Because each face of the cube is two-dimensional, we must convert cm¶ to cm². A cm¶ is not a standard unit for area; this appears to be a typo or error in the expression given. Instead, let's find the length of the side (s) of the cube by taking the cube root of the volume: ∛(8 cm³) = 2 cm. Then, calculate the area (A) of a face using A = s² = (2 cm)² = 4 cm².