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. we know • • • c. will janelle use wrapping paper exactly the size of the surface area of the box? explain your answer.

Explanation:

Step1: Identify surface - area formula

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

Step2: Calculate area of end - faces

The area of each end - face (square) is $A_{end}=s^2$, where $s = 15$ cm. So $A_{end}=15\times15=225$ $cm^2$. The total area of the two end - faces is $2\times225 = 450$ $cm^2$.

Step3: Calculate area of side - faces

The area of each of the four side - faces (rectangles) is $A_{side}=l\times s$, where $l = 30$ cm and $s = 15$ cm. So $A_{side}=30\times15 = 450$ $cm^2$. The total area of the four side - faces is $4\times450=1800$ $cm^2$.

Step4: Calculate total surface area

The total surface area $SA=450 + 1800=2250$ $cm^2$.

For part c:

In real - life, Janelle will likely need more wrapping paper than the surface area of the box. This is because she needs extra paper for overlapping and folding to secure the paper around the box.

Answer:

b. $2250$ $cm^2$
c. No. In real - life, extra paper is needed for overlapping and folding to secure the wrapping paper around the box.