a smaller box has dimension that half the measurements of the orignal . find the ratio of the surface area of the orginal box to the surface area of the smaller box
To find the ratio of the surface area of the original box to the surface area of the smaller box, we need to compare their surface areas.
Let's assume the original box has dimensions length (L), width (W), and height (H). The surface area of the original box can be calculated using the formula:
Surface area of original box = 2(LW + LH + WH)
Now the smaller box has dimensions that are half the measurements of the original box. So, the dimensions of the smaller box are L/2, W/2, and H/2.
To find the surface area of the smaller box, we use the same formula:
Surface area of smaller box = 2((L/2)(W/2) + (L/2)(H/2) + (W/2)(H/2))
Now we can calculate the ratio:
Ratio = Surface area of original box / Surface area of smaller box
Ratio = [2(LW + LH + WH)] / [2((L/2)(W/2) + (L/2)(H/2) + (W/2)(H/2))]
Simplifying the equation:
Ratio = (LW + LH + WH) / ((L/2)(W/2) + (L/2)(H/2) + (W/2)(H/2))
Ratio = (LW + LH + WH) / [(LW + LH + WH)/2]
Ratio = 2
Therefore, the ratio of the surface area of the original box to the surface area of the smaller box is 2.