A set designer is wrapping 2 boxes for stage props. She needs to reduce the size of 1 box by making each linear dimension 75% less. She used N in. 2 of wrapping paper to cover the outside surface of the original box. How many square inches of wrapping paper will cover the outside surface of the smaller box?

The answer to the question is 9/16 N² in.

9/16 N square inches of wrapping paper will cover the outside surface of the smaller box.

Step-by-step explanation:

To solve the question, we note that the initial area of the wrapper is given by

a * a * 6 as the box has 6 sides

Therefore 6·a² = N² in. = The original are of the wrapper

When the size of the box is reduced to 75 % we have

Side of new wrapper = 0.75 * a = 3/4*a

Therefore the area is given by

3/4*a * 3/4*a * 6 = 9/16*a²*6 = 27/8 a²

Therefore the area to cover the box is (27/8) / 6 N² = 9/16 N² or 0.5625 N² in.