Question

calculate the surface area of a rectangular prism 16 x 14 x 6 and the wrapping paper measures 25 x 405, how many boxes can be wrapped

Answer 1

To calculate the surface area of a rectangular prism, you can use the formula:

\[
\text{Surface Area} = 2(lw + lh + wh)
\]

where \( l \), \( w \), and \( h \) are the length, width, and height of the prism.

Given the dimensions of the prism:
- Length (\( l \)) = 16
- Width (\( w \)) = 14
- Height (\( h \)) = 6

Let's calculate the surface area:

\[
\text{Surface Area} = 2(16 \times 14 + 16 \times 6 + 14 \times 6)
\]

Calculating each term:

1. \( 16 \times 14 = 224 \)
2. \( 16 \times 6 = 96 \)
3. \( 14 \times 6 = 84 \)

Now plug these values back into the formula:

\[
\text{Surface Area} = 2(224 + 96 + 84) = 2(404) = 808
\]

The surface area of the rectangular prism is **808 square units**.

Next, let's determine how many boxes can be wrapped with the given dimensions of the wrapping paper, which measures 25 x 405.

First, calculate the total area of the wrapping paper:
\[
\text{Area of Wrapping Paper} = \text{Length} \times \text{Width} = 25 \times 405 = 10125 \text{ square units}
\]

Now, divide the total area of the wrapping paper by the surface area of one box to find out how many boxes can be wrapped:

\[
\text{Number of Boxes} = \frac{\text{Area of Wrapping Paper}}{\text{Surface Area}} = \frac{10125}{808}
\]

Calculating this gives:

\[
\text{Number of Boxes} \approx 12.5
\]

Since you can't wrap half a box, you can wrap **12 boxes** with the available wrapping paper.