Final answer:
To determine which cube has the larger surface area, we convert the side lengths and calculate the surface areas for each cube using the formula for a cube. The cube with side length 13.12ft has the largest surface area.
Step-by-step explanation:
To determine which cube has the larger surface area, we need to convert the side lengths to the same unit of measure. Given the conversion factor 3.28ft/1m, we can convert the side lengths for each cube:
a) Cube with side length 2 meters: 2m * 3.28ft/m = 6.56ft
b) Cube with side length 6 feet: 6ft / 3.28ft/m = 1.83m
c) Cube with side length 4 meters: 4m * 3.28ft/m = 13.12ft
d) Cube with side length 10 feet: 10ft / 3.28ft/m = 3.05m
Now we can calculate the surface area for each cube using the formula for a cube: SA = 6s², where s is the side length.
a) Cube with side length 6.56ft: SA = 6 * (6.56ft)² = 256.51ft²
b) Cube with side length 1.83m: SA = 6 * (1.83m)² = 20.41m²
c) Cube with side length 13.12ft: SA = 6 * (13.12ft)² = 1074.18ft²
d) Cube with side length 3.05m: SA = 6 * (3.05m)² = 55.80m²
Comparing the surface areas, we can see that c) Cube with side length 13.12ft has the largest surface area.