If the volume of a cube is (8 x $10^3$)cm$^3$, what is the surface area of the cube?

Analyze the question: We are given the volume of a cube, 8 × 10³ cm³ = 8,000 cm³, and we must find the total surface area.

Concept:

• Volume of a cube = s³, where s is the side length
• Surface area of a cube = 6s² (a cube has 6 equal square faces)

Solution:

Step 1: Find the side length. s³ = 8 × 10³ s = ∛8 × ∛(10³) = 2 × 10 = 20 cm

Step 2: Find the surface area. Surface area = 6s² = 6 × 20² = 6 × 400 = 2,400 cm²

Answer: The surface area is 2,400 cm², which is option A.

Tip: When the volume is written as a number × 10³, take the cube root of each part separately. Here ∛8 = 2 and ∛(10³) = 10, so s = 20 right away. Also remember that the surface area of a cube is 6s², not s² or 4s².