Will you please attempt this question!?? Exam is tomorrow and I need your help!Two cuboids are mathematically similar. The smaller one has a...

Given the smaller cuboid has a surface area 400
cm^3

Let the dimensions be
5*x1*y1

Then the surface area is given
by:

SA = 2*5x + 2*5y + 2*xy =
400

==> 10x1 + 10y1 + 2x1y1 = 400
..............(1)

Now the larger
cuboid.

==> SA = 2*8x2 + 2*8y2 +
2*x2*y2

==> SA = 16x2 + 16y2 +
2x2y2..............(2)

But since both cuboids are similar ,
then we know that:

x1/x2 = 5/8==> x2= 8/5
x1

 y1/y2 = 5/8 ==> y2 = 8/5
y1

Now we will substitute into
(2)

==> SA = 16(8/5)x1 + 16(8/5)y1 +
2(8/5)(8/5)x1y1

==> SA = (128/5)x1 + (128/5)y1 +
(128/25)x1y1

Now factor
128/5

==> SA = (128/5)*[ x1 + y1 +
(1/5)x1y1]

Now multiply and divide by
10.

==> SA = (128/10*5) [ 10x1+ 10y1 +
2x1y1]

But. from (1),  we know that 10x1+10y1 + 2x1x2 =
400

==> SA = 128/50 * 400 =
1024

Then the surface area is 1024
cm^2