Final answer:
To find the surface area of the large jewelry box, we need to apply the given information and use the formula for the surface area of a rectangular prism. By substituting the known values and solving the equation, the surface area of the large box is found to be approximately 6.11 cm².
Step-by-step explanation:
To find the surface area of the large jewelry box, we need to apply the given information. Let's say the dimensions of the small jewelry box are length (L), width (W), and height (H). The surface area of a rectangular prism is given by the formula:
SA = 2(LW + LH + WH)
Given that the surface area of the small jewelry box is 110 cm², we can substitute the known values into the formula:
110 = 2(LW + LH + WH)
Next, we determine the dimensions of the large jewelry box. According to the problem, the dimensions of the large box are three times the dimensions of the small box:
Length of large box = 3L, Width of large box = 3W, Height of large box = 3H
Now, substitute these values into the surface area formula for the large box:
SA of large box = 2((3L)(3W) + (3L)(3H) + (3W)(3H)) = 2(9LW + 9LH + 9WH) = 18(LW + LH + WH)
Simplify this equation:
SA of large box = 18(LW + LH + WH)
Since we know the surface area of the small box is 110 cm², we can use this to find the surface area of the large box:
18(LW + LH + WH) = 110
Solving for the surface area of the large box:
LW + LH + WH = 110/18 = 6.11 cm²
Therefore, the surface area of the large jewelry box is approximately 6.11 cm².