Question

A cubic wooden block with a side length of 8 inches is painted red using 1 pint of paint. If the block is then cut into cubes of side length 4 inches, what is the minimum amount of paint that is needed to color all the smaller cubes red?

• A. 1 pint
• B. 2 pints
• C. 3 pints
• D. 4 pints

Answer 1

The correct option is A 1 pint

$Totalnumberofsmallercubesthatcanbeformedfromthebigcube:$

$=\frac{Volumeofbigcube}{Volumeofsmallercube}=\frac{(8\times 8\times 8)i{n}^3}{(4\times 4\times 4)i{n}^3}=2\times 2\times 2=8$

Picturing the smaller cubes cut from the big cube, we get:


As we can see, 3 faces of each smaller cube are already painted red.


$Totalnumberoffaces=6⟹Numberofunpaintedfacesoneachsmallercube=6–3=3$

$Totalnumberofunpaintedfaces=Totalnumberofsmallercubes\times 3=8\times 3=24$

$Areaofeachfaceofthesmallercubes=4units\times 4units=16squnits$

$⟹Totalunpaintedarea=24\times 16=384squnits$

Now, the entire surface area of the bigger cube is painted red. Hence, calculating the painted area of the bigger cube, we find:

$Paintedareaofthebiggercube=Surfaceareaofthebiggercube=6\times Areaofeachface=6\times (8units\times 8units)=384squnits$

Hence, we have:

$Totalunpaintedareaofthesmallercubes=Totalpaintedareaofthebiggercube$

Now, to paint the bigger cube red, 1 pint of paint was used. So, to paint all the unpainted faces of the smaller cubes, an additional pint of paint is required.