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

Explanation:

Part (a)

Step1: Recall surface area formula for rectangular prism

The formula for the surface area \( SA \) of a rectangular prism with length \( l \), width \( w \), and height \( h \) is \( SA = 2(lw + lh + wh) \). Here, \( l = 15 \) ft, \( w = 13 \) ft, \( h = 2 \) ft.

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So surface area is \( 502\space ft^2 \).

Step2: Recall volume formula for rectangular prism

The formula for the volume \( V \) of a rectangular prism is \( V=l\times w\times h \).

$$ V = 15\times13\times2=390 $$

So volume is \( 390\space ft^3 \).

Part (b)

To find the amount of sand a box can hold, we need to know the space inside the box, which is given by volume (as volume measures the amount of space occupied or can be occupied by a substance). Surface area measures the total area of the outer surfaces, which is not related to the capacity to hold sand.

To know how much wood to buy for making the box, we need to know the total area of the wood required to make the outer surfaces of the box (including the lid). This is given by surface area. Volume is about the space inside, not the material needed for the structure.

Answer:

Volume

Part (c)