Question

cathy wants to pack 100 gifts. the packaging includes a closed box made out of cardboard. the dimensions of the box are 16 cm long, 8 cm wide and 8 cm high. in square centimeters, what is the minimum amount of cardboard cathy needs to package all the gifts?
drag & drop the answer
38400 cm²
39200 cm²
48000 cm²
note: use ctrl+d to drag the option via keyboard
amount of cardboard required:

Explanation:

Step1: Find surface area of 1 box

The formula for the surface area of a closed rectangular box is $SA = 2(lw + lh + wh)$, where $l=12\ \text{cm}$, $w=8\ \text{cm}$, $h=8\ \text{cm}$.
$$SA = 2((12\times8)+(12\times8)+(8\times8))$$
$$SA = 2(96 + 96 + 64)$$
$$SA = 2\times256 = 512\ \text{cm}^2$$

Step2: Calculate total cardboard for 100 boxes

Multiply single box surface area by 100.
$$\text{Total SA} = 512\times100 = 39200\ \text{cm}^2$$

Answer:

$39200\ \text{cm}^2$