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**+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) ) cm^{2}

= 2( 15 + 18 + 30 ) cm^{2}

= 2( 63 ) cm^{2}

= 126 cm^{2}

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

each cube has a surface area of 6 cm^{2}

total surface area of all the cubes = 90 * 6 cm^{2} = 540 cm^{2}

the area of the unpainted surfaces

= total surface area - the painted area

= 540 cm^{2} - 126 cm^{2}

= 414 cm^{2}

hectictar
Feb 14, 2018

#2**+2 **

Best Answer

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) ) cm^{2}

= 2( 15 + 18 + 30 ) cm^{2}

= 2( 63 ) cm^{2}

= 126 cm^{2}

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

each cube has a surface area of 6 cm^{2}

total surface area of all the cubes = 90 * 6 cm^{2} = 540 cm^{2}

the area of the unpainted surfaces

= total surface area - the painted area

= 540 cm^{2} - 126 cm^{2}

= 414 cm^{2}

hectictar
Feb 14, 2018