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?
+9481 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
+9481 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
