Question

Santana wants to cover a gift box shaped like a rectangular prism the foil costs $0.03 per square inch. santana has a choice between box a which is 8 inches long, 3 inches wide, and 6 inches high. box b is 10 inches long, 3 inches wide, and 4 inches wide. which box will be less expensive to cover with foil, and by how much?

Answer 1

The answer is box b, by $0.48

Calculate the surface area of rectangular prism is A = 2 (wl + hl + wh)
w - width, l - length, h - height
The cost is $0.03 per square inch: C = .0.03 * A

Box a:
l = 8 in
w = 3 in
h = 6 in
A = 2 (wl + hl + wh) = 2(3 * 8 + 6 * 8 + 3 * 6) = 2(24 + 48 + 18) = 2 * 90 = 180 in²
C = 0.03 * A = 0.03 * 180 = $5.40

Box b:
l = 10 in
w = 3 in
h = 4 in
A = 2 (wl + hl + wh) = 2(3 * 10 + 4 * 10 + 3 * 4) = 2(30 + 40 + 12) = 2 * 82 = 164 in²
C = 0.03 * A = 0.03 * 164 = $4.92

Thus, it is less expensive to cover box b with foil by $5.40 - $4.92 = $0.48