Answer:
Volume = 1870 in³ for all boxes
Surface area = 934 in² for the selected box
Step-by-step explanation:
Each ream of paper weight 5 pounds, so if we want to reduce the box by 10 pounds, we need to use 2 reams less on each box because
5 pounds x 2 = 10 pounds
Then, each box will have 10 reams. So, the possibilities for the box are
1 stack of 10 reams
10 stacks of 1 ream
2 stacks of 5 reams
5 stacks of 2 reams
Considering the ease with which one person can carry the box, we will recommend 2 stacks of 5 reams, because the measure of the box will be
Width = Width of ream x 2
Width = 8.5 in x 2
Width = 17 in
Length = Lenght of a ream
Length = 11 in
Length = 11 in
Height = Height of ream x 5
Height = 2 in x 5
Height = 10 in
Therefore, the volume of this box will be
Volume = Width x Length x Height
Volume = 17 in x 11 in x 10 in
Volume = 1870 in³
So, the volume of the box is 1870 in³. We can also say that no matter the dimensions of the box, the volume will always be 1870 in³ because the space occupied by each box will be the space of 10 reams.
Then, to calculate the surface area we will use the following equation:
Surface area = 2(Length x Width) + 2(Length x Height) + 2(Width x Height)
Surface area = 2(11 in x 17 in) + 2(11 in x 10 in) + 2(17 in x 10 in)
Surface area = 2(187 in²) + 2(110 in²) + 2(170 in²)
Surface area = 374 in² + 220 in² + 340 in²
Surface area = 934 in²
If we calculate the surface area for another box, for example 10 stacks of 1 ream, we will get:
Width = 8.5 in
Length = 11 in
Width = 2 in x 10 = 20 in
Surface area = 2(11 in x 8.5 in) + 2(11 in x 20 in) + 2(8.5 in x 20 in)
Surface area = 967 in²
Therefore, when we change the box, the surface area changes because it depends on the length, width and height of the box.