Question

(a) use the calculator to find the surface area and volume of the brick. make sure to include the correct units.
surface area:
volume:
(b) the brick will be gold - plated (dipped in gold). which measure would be used to find the amount of gold needed?
surface area volume
(c) the brick will be painted. which measure will help the painter know how much paint to buy?
surface area volume

Explanation:

Step1: Recall surface - area formula for a rectangular prism

The surface - area formula of a rectangular prism is $SA = 2(lw+lh + wh)$, where $l = 7$ cm, $w = 6$ cm, and $h = 5$ cm.
$SA=2(7\times6 + 7\times5+6\times5)$

Step2: Calculate the values inside the parentheses

$7\times6=42$, $7\times5 = 35$, $6\times5=30$. Then $7\times6 + 7\times5+6\times5=42 + 35+30=107$.
$SA = 2\times107=214$ cm²

Step3: Recall volume formula for a rectangular prism

The volume formula of a rectangular prism is $V=lwh$.
$V = 7\times6\times5$

Step4: Calculate the volume

$7\times6\times5=210$ cm³

Step5: Determine amount of gold needed

The amount of gold needed to gold - plate the brick is related to the surface area of the brick, because gold covers the outer surface.

Step6: Determine amount of paint needed

The amount of paint needed to paint the brick is related to the surface area of the brick, as paint covers the outer surface.

Answer:

(a) Surface area: $214$ cm²
Volume: $210$ cm³
(b) Surface area
(c) Surface area