Question

How much surface area would be lost if you glued three 4-cm cubes together to make a rod that is three cubes long and one cube wide?

Answer 1

Answer:

Part 3) $SA=288\ cm^2$

Part 4) $64\ cm^2$

Step-by-step explanation:

Part 3) Calculate the total surface area of three 4 cm cubes

we know that

The surface area of a cube is equal to the area of its six square faces

$SA=6b^2$

so

The surface area of three cubes is equal to the area of its 18 square faces

$SA=18b^2$

where

b is the length side of the square face

In this problem

$b=4\ cm$

so

The surface area of three cubes is

$SA=18b^2$

substitute the given value

$SA=18(4)^2$

$SA=288\ cm^2$

Part 4) How much surface area would be lost if you glued three 4-cm cubes together to make a rod that is three cubes long and one cube wide?

In this case the total surface area of the three glued 4-cm cubes is equal to the area  of  its 14 square faces

so

The surface area lost is equal to

$18b^2-14b^2=4b^2$

substitute

$4(4)^2=64\ cm^2$