Question

Roberta is wrapping gift boxes. Each gift box is a rectangular prism with a square base of side 8 inches. The difference between the heights of the two gift boxes is 9 inches.

If the larger box has a surface area of 544 square inches, what is the difference in the surface area of the two boxes?

A) 576 square inches

B) 648 square inches

C) 324 square inches

D) 288 square inches

Answer 1

Let "x" = the height of the larger box. Therefore, "x-9" = the height of the smaller box.

SL = Surface area or the larger, SS = Surface area of the smaller.

SL = (2)(8^2) + (4)(8)(x) = 544

So, just solve for "x"

SS = SL = (2)(8^2) + (4)(8)(x - 9)

Difference = SL - SS

Answer 2

how do i solve for x?

Answer 3

What course are you in?

Answer 4

geometry i just dont remember doing this since its been forever since i had to deal with this sort of problem

Answer 5

Do you know how to square a number?

Answer 6

yes

Answer 7

i just dont remember how to solve for x when there isnt a number on the other side of the equal sign

Answer 8

Then take equation:

SL = (2)(8^2) + (4)(8)(x) = 544

and start by squaring the "8". You will progressively simplify the equation.

Answer 9

oh ok

Answer 10

x = 22

Answer 11

An even easier way to solve this problem is to realize that the base area for the top and bottom surfaces is the same and the difference in surface area lies in:

(4)(8)(x) - (4)(8)(x - 9) = (4)(8)(9) = D

Answer 12

thanks

Answer 13

You're welcome and thx for the recognition!