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# Find the surface area of the unpainted sides

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A rectangular prism 3cm x 5cm x 6cm is painted mauve and is then cut into 1cm^3 cubes. What is the total unpainted surface area of these cubes?

Guest Feb 14, 2018

#2
+6362
+2

If you want the area of all the unpainted surfaces...

the painted area

=   the surface area of the prism

=   2( (3)(5) + (3)(6) + (5)(6) )  cm2

=   2( 15 + 18 + 30 )  cm2

=   2(  63 )  cm2

=   126  cm2

the number of cubes   =   3 * 5 * 6   =   90

each cube has a surface area of  6  cm2

total surface area of all the cubes   =   90 * 6  cm2   =   540 cm2

the area of the unpainted surfaces

=   total surface area - the painted area

=   540 cm2 - 126 cm2

=   414 cm2

hectictar  Feb 14, 2018
Sort:

#1
+82916
0

Nvm..I read this incorrectly....hectictar spotted my error....I told her to post her solution

CPhill  Feb 14, 2018
edited by CPhill  Feb 14, 2018
#2
+6362
+2

If you want the area of all the unpainted surfaces...

the painted area

=   the surface area of the prism

=   2( (3)(5) + (3)(6) + (5)(6) )  cm2

=   2( 15 + 18 + 30 )  cm2

=   2(  63 )  cm2

=   126  cm2

the number of cubes   =   3 * 5 * 6   =   90

each cube has a surface area of  6  cm2

total surface area of all the cubes   =   90 * 6  cm2   =   540 cm2

the area of the unpainted surfaces

=   total surface area - the painted area

=   540 cm2 - 126 cm2

=   414 cm2

hectictar  Feb 14, 2018
#3
+82916
+1

Thanks, hectictar  !!!

CPhill  Feb 14, 2018

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