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 was made from wood. which measure helped the carpenter know how much wood to buy?
○ surface area ○ volume
(c) the box needs to be painted. which measure will help the carpenter know how much paint to buy?
○ surface area ○ volume

Explanation:

Step1: Define prism dimensions

Length $l=10$ ft, width $w=14$ ft, height $h=2$ ft

Step2: Calculate surface area (with lid)

Formula: $2(lw + lh + wh)$

$$\begin{align*} &2((10\times14)+(10\times2)+(14\times2))\\ =&2(140 + 20 + 28)\\ =&2\times188\\ =&376 \end{align*}$$

Step3: Calculate volume

Formula: $l\times w\times h$
$10\times14\times2=280$

Step4: Answer part (b) logic

Wood needed depends on material amount (surface area).

Step5: Answer part (c) logic

Paint needed depends on area to cover (surface area).

Answer:

(a)
Surface area: $376$ ft²
Volume: $280$ ft³
(b) Surface area
(c) Surface area