Question

A roll of wrapping paper measures 25 in. × 405 in. The boxes being wrapped are 16 in. × 14 in. × 6 in. How many complete boxes can be wrapped with one roll of wrapping paper

Answer 1

To find how many boxes can be wrapped, calculate the surface area of one box and divide the total area of the wrapping paper roll by that number. A box measuring 16 in. × 14 in. × 6 in. has a surface area of 808 in.², and the roll of paper is 10,125 in.², so 12 complete boxes can be wrapped.

Step-by-step explanation:

To determine how many complete boxes can be wrapped with a roll of wrapping paper measuring 25 inches by 405 inches, we first need to calculate the surface area of the box to be wrapped. A box with dimensions 16 in. × 14 in. × 6 in. has three different pairs of sides. Each pair of sides will be wrapped, so we calculate the total surface area of the box by adding the areas of each pair:

Top/Bottom (16 in. × 14 in.) × 2 = 448 in.²

Front/Back (14 in. × 6 in.) × 2 = 168 in.²

Sides (16 in. × 6 in.) × 2 = 192 in.²

Adding these areas together gives us the total surface area needed to wrap one box:

448 in.² + 168 in.² + 192 in.² = 808 in.²

Now let's find the total area of the wrapping paper roll:

25 in. × 405 in. = 10,125 in.²

To find how many boxes can be wrapped, we divide the total area of the wrapping paper by the surface area needed for one box:

10,125 in.² ÷ 808 in.² = 12.52

Since we cannot wrap a fraction of a box, we can only wrap 12 complete boxes with the roll of wrapping paper.

Answer 2

Approximately 11 complete boxes can be wrapped with one roll of wrapping paper.

Step-by-step explanation:

To determine the number of complete boxes that can be wrapped with one roll of wrapping paper, we need to calculate the amount of wrapping paper needed to wrap one box and then divide the total amount of wrapping paper by this value.

The surface area of the box is given by 2(length × width + width × height + length × height).

In this case, it is 2(16 × 14 + 14 × 6 + 16 × 6)

= 872 in².

The surface area of the wrapping paper is 25 × 405

= 10,125 in².

Dividing the surface area of the wrapping paper by the surface area of the box, we get:

10,125 in² ÷ 872 in²

≈ 11.6.

Therefore, approximately 11 complete boxes can be wrapped with one roll of wrapping paper.