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?
110 square inches
240 square inches
300 square inches
720 square inches

Answer 1

@dpaInc Could you please look at this?

Answer 2

@AccessDenied Do you mind looking at this?

Answer 3

I'll try to do this step by step. Let me know if anything's unclear.

The surface area is the sum of the area of all sides. For the rectangular prisms in this question, the two square faces have the same surface area and the four rectangular faces have the same surface area (i.e. SA = 2S + 4R).

The squares faces are the same for both boxes and have a surface area of 12^2 = 144 square in each, so SA = 288 + 4R for both boxes.

One box is 5 inches taller than the other (corresponding to the length of the rectangular faces). For the shorter box, each rectangular face has an area of 12x, while those of the larger box have an area each have an area of 12(x+5). Also, we know the large box has a total surface area of 624 square inches, so now:

Small box: SA = 288 + 4*12x
Large box: 624 = 288 + 4*12(x+5)

Notice we can solve for x using the large box equation. Doing this, you should get x = 2, which is the height of the small box. Now we can calculate the SA of the small box using this value to get 384 square inches.

The difference in SA between the two boxes is 624-384 = 240 square inches.

Answer 4

That was very helpful! Thank you!

Answer 5

np glad I could help :)