Question

Jeremy made one vertical stack of boxes that had a surface area of 17,052 square centimeters. How many shoe boxes were in the stack?

Answer 1

there are 7 boxes in the stack.

Explanation:

After a quick online search, I've found that the dimensions of each box are:

Height = H = 18cm

Length = L = 40cm

Width = W = 21cm

If we stack the boxes, then the only thing that changes in the figure is the height, so if we stack N boxes, the dimensions will be:

Height = H = N*18cm

Length = L = 40cm

Width = W = 21cm

And for a rectangular prism of height H, width W, and length L, the surface is:

S = 2*(H*W + W*L + H*L)

Then for our stack of boxes, the surface is:

S = 2*(40cm*21cm + 40cm*N*18cm + 21cm*N*18cm)

And we know that the total surface is 17,052 cm^2

Then we just need to solve:

2*(40cm*21cm + 40cm*N*18cm + 21cm*N*18cm) = 17,052 cm^2

(40cm*21cm + 40cm*N*18cm + 21cm*N*18cm) = (17,052 cm^2)/2

(40cm*21cm + 40cm*N*18cm + 21cm*N*18cm) = 8,526 cm^2

840 cm^2 + N*720 cm^2 + N*378 cm^2 = 8,526 cm^2

N*(720 cm^2 + 378 cm^2) = 8,526 cm^2 - 840 cm^2 = 7,686 cm^2

N*(1,098 cm^2) = 7,686 cm^2

N = (7,686 cm^2)/(1,098 cm^2) = 7

So there are 7 boxes in the stack.