Question

the figure below shows a hollow box in the shape of a rectangular prism. note that the box has a lid. (a) use the calculator to find the surface area and volume of the box. make sure to include the correct units. surface area: volume: (b) the box is to be filled with sand. which measure would be used to find the amount of sand the box will hold? o surface area o volume (c) the box was made from wood. which measure helped the carpenter know how much wood to buy? o surface area o volume

Explanation:

Step1: Recall surface - area formula

The surface - area formula of a rectangular prism is $SA = 2(lw+lh + wh)$, where $l = 15$ ft, $w = 13$ ft, and $h = 2$ ft.
$SA=2(15\times13 + 15\times2+13\times2)$

Step2: Calculate the products inside the parentheses

$15\times13 = 195$, $15\times2 = 30$, $13\times2 = 26$. Then $195 + 30+26=251$.
$SA = 2\times251=502$ ft²

Step3: Recall volume formula

The volume formula of a rectangular prism is $V=lwh$.
$V = 15\times13\times2$

Step4: Calculate the volume

$15\times13\times2=390$ ft³

Step5: Answer part (b)

The volume measures the space inside the box, so to find the amount of sand the box will hold, we use volume.

Step6: Answer part (c)

The surface - area measures the total area of the outer faces of the box. So, to know how much wood to buy to make the box, we use surface area.

Answer:

(a) Surface area: $502$ ft²
Volume: $390$ ft³
(b) Volume
(c) Surface area