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

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

Part 4)
`64\ cm^2`

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`