A laundry soap company decides it wants to shrink the size of its box to save on cost. The surface area of the original box is 112 cm2 . If it creates a new box using a scale factor of 34 , determine the surface area of the new box. Round to the nearest tenth if necessary.
The scale factor is 34, which means the new box will have dimensions that are 34 times smaller than the original box.
Let's call the dimensions of the original box length (L), width (W), and height (H).
The surface area of the original box is given by SA = 2(LW + LH + WH) = 112 cm^2.
Since the new box has dimensions that are 34 times smaller, we can write the new dimensions as L' = L/34, W' = W/34, and H' = H/34.
The surface area of the new box can be calculated in a similar manner:
SA' = 2(L'W' + L'H' + W'H').
Substituting the new dimensions, we get:
SA' = 2((L/34)(W/34) + (L/34)(H/34) + (W/34)(H/34)).
Simplifying,
SA' = 2(LWH/34^2).
Since the surface area of the new box is SA' = SA/34^2, we can calculate it as follows:
SA' = 112 cm^2 / (34^2) ≈ 0.924 cm^2.
Therefore, the surface area of the new box is approximately 0.9 cm^2.