Question

Amelie wants to decorate the outside of the box but not the bottom. It is a 5 in. by 3 in. by 2 rectangular prism. If the beads that she is using cost $0.25 per square inch, how much will she pay for the beads? Her work is shown. surface area = 15 + 15 + 6 + 6 + 10 + 10 = 62 in. 2 cost = 0.25(62) = $15.50 Did she make an error? Yes, she should have only added the area of five of the six faces. Yes, she did not use the correct area formula for a rectangle. Yes, she calculated the cost incorrectly. No, she didn’t make any errors.

Answer 1

Yes, she should have only added the area of five of the six faces.

Explanation:

The formula for determining the surface area of a cuboid or box is expressed as

Surface area = 2lw + 2lh + 2wh

Where l, w and h represents length, width and height of the box respectively.

2lw represents the area of the top and the bottom of the box. Since she doesn't want to cover the bottom, it becomes lw. Therefore,

Surface area = 15 + 6 + 6 + 10 + 10 = 47 in².

The cost would be

0.25 × 47 = $11.75

Therefore,

Yes, she should have only added the area of five of the six faces.