A cube has sides of length 3 nm. What are the surface area and volume of the cube?

• A. Surface area: 27 nm^2; Volume: 9 nm^3
• B. Surface area: 36 nm^2; Volume: 18 nm^3
• C. Surface area: 18 nm^2; Volume: 9 nm^3
• D. Surface area: 54 nm^2; Volume: 27 nm^3

Answer: (D)

Verified step by step guidance

1. Identify the formula for the surface area of a cube: \(SA = 6 \times a^2\), where \(a\) is the length of one side of the cube.
2. Identify the formula for the volume of a cube: \(V = a^3\), where \(a\) is the length of one side of the cube.
3. Substitute the given side length \(a = 3\) nm into the surface area formula: \(SA = 6 \times (3\, \text{nm})^2\).
4. Substitute the given side length \(a = 3\) nm into the volume formula: \(V = (3\, \text{nm})^3\).
5. Calculate the numerical values for surface area and volume using the substituted expressions to find the correct answer.