Question

1. janelle is wrapping a present in a rectangular box. the box is 30 cm long and has a square on each end (15 cm by 15 cm).

a. draw a 3 - d diagram and net of the box including dimensions.
b. determine the surface area of the box. remember to include units.

Explanation:

Step1: Identify the surface - area formula for a rectangular prism

The formula for the surface area of a rectangular prism is $SA = 2(lw+lh + wh)$, where $l$ is the length, $w$ is the width, and $h$ is the height. In this case, $l = 30$ cm, $w=15$ cm, and $h = 15$ cm.

Step2: Calculate the area of each type of face

There are two square faces with area $A_{square}=w\times h=15\times15 = 225$ $cm^{2}$, and four rectangular faces with area $A_{rectangle}=l\times w=30\times15 = 450$ $cm^{2}$.

Step3: Calculate the total surface area

$SA=2\times A_{square}+4\times A_{rectangle}$. Substitute the values: $SA = 2\times225+4\times450$. First, $2\times225 = 450$ and $4\times450=1800$. Then $SA=450 + 1800=2250$ $cm^{2}$.

Answer:

$2250$ $cm^{2}$