Question

the figure below shows a brick in the shape of a rectangular prism.
(6 cm, 14 cm, 8 cm diagram)
(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:

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, \( l = 14 \) cm, \( w = 8 \) cm, \( h = 6 \) cm.

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So surface area is \( 488 \) square centimeters.

Step2: Recall volume formula for rectangular prism

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

$$ V = 14\times8\times6=672 $$

So volume is \( 672 \) cubic centimeters.

Step3: Recall gold - plating concept (for part b)

Gold - plating covers the outer surface of the brick. So the amount of gold needed depends on the surface area of the brick.

Step4: Recall painting concept (for part c)

Paint is applied on the outer surface of the brick. So the amount of paint needed depends on the surface area of the brick.

Part (b)

Gold - plating involves covering the outer surface of the brick. The surface area measures the total area of the outer surfaces. Volume measures the space inside the brick, which is not relevant for gold - plating. So surface area is used.

Painting is done on the outer surface of the brick. The surface area gives the total area to be painted. Volume is about the space inside, not relevant for painting. So surface area is used.

Answer:

Surface area

Part (c)