Question

Gillian is wrapping gift boxes. Each gift box is a rectangular prism with a square base of side 12 inches. The difference between the heights of the two gift boxes is 5 inches.

If the larger box has a surface area of 624 square inches, what is the difference in the surface area of the two boxes?

A. 110 square inches
B. 240 square inches
C. 300 square inches
D. 720 square inches.

Answer 1

it would be B: 240 square inches
using the formula of the surface area = 2lw + 2wh + 2lh
entering what we already know, and solving for h; to find out what is the height
624 = 2(12)(12) + 2(12)(h) + 2(12)(h)
624 = 288 + 24h + 24h
624 = 288 + 48h
624 - 288 = 48h
336 = 48h
336/48 = h
h = 7
so since their is a 5 inch difference and this is the larger box, the other would be 7 - 5 = 2
so we do the same procedures though now for the height we put 2 and we solve for the surface area.
SA = 2lw + 2wh + 2lh
SA = 2(12)(12) + 2(12)(2) + 2(12)(2)
SA = 288 + 48 + 48
SA = 384
Now we are looking for the difference between the two so;
624 - 384 = difference
240 = difference
the answer is 240 square inches

Answer 2

Thank you so much!

Answer 3

np (: