PLEASE ANSWER THIS MATH question!! I beg of you!You will be a lifesaver XD?

Question

The outside surfaces of a cube is painted blue.
It is 6 by 6 by 6.
The cube is cut into 27 congruent cubes.
A)Calculate the surface area of the painted surface of the small cubes.
B)Calculate the surface area of the unpainted surface of the small cubes.

Answer 1

singing light: Daniel A sounds like a good catch. The smart ones usually have very good earning potential

Answer 2

The answer is 432 square units of unpainted surface area.
The following steps are how I got it:

First we need to find the volume of the cube:
6*6*6=216 cubic unit

The volume of each of the 27 cubes should be:
216/27=8 cubic unit

Now
8=2*2*2
which gives the sides of the little cubes.

The surface area of each side of the little cube should be :
2*2=4 square unit.

Out of the 27 cubes, the corner edge cubes have 3 side surfaces unpainted, that means:
3*8=24 surfaces unpainted
Then multiply by the area of each surface
24*4=96 square unit area of the corner edge cubes are unpainted.

The center edge cubes have 4 side surfaces unpainted:
4*12=48*4=192 square unit area of the middle edge cubes are unpainted.

The center middle cubes each have 5 internal surfaces unpainted:
5*6=30*4=120 square unit unpainted

The central cube is entirely unpainted:
1*6*4=24 square unit

Now if we add all the 27 (8+12+6+1) cube surface areas, we get the unpainted surface area of the small cubes:

96+192+120+24=432 square unit area unpainted

If we multiply the volume of the container cube 216 by 2 we get the equivalent of the unpainted area 432 but I can't prove if this can be used as a general formula.

Answer 3

The 27 cubes will have the same area painted as the the large cube which is 6^3 = 216 units ^2.
The 8 corner cubes will have three of their sides painted and three of their sides unpainted. The 12 cubes between the corner cubes will have two sides painted and 4 sides unpainted. The 6 cubes in the center of eack side will have 1 side painted and 5 sides unpainted. The 1 cube in the center will have no sides painted.

Thus the number of unpainted sides is 1*6 + 6*5 + 12*4+ 8*3 = 108. Each side is 2^2= 4 units^2. So totalmunpainted area is 4*108 = 432 units^2.

Answer 4

The surface area of painted is going to be the same as the surface area of the original cube:

6 x 6 x 6 = 216 units^2

Each of the 27 congruent cubes will be 2 x 2 x 2 and therefore will have a total surface area of 27 x 6 x 2 x 2 = 648 units^2
To find unpainted area subtract the first from the second:
648 - 216 = 432 units^2

Answer 5

OK, this sounds like a bit of a trick question. The painted surface area is 6 * (6*6) = 216; when the cube is cut into smaller cubes, this value can't change so the surface area of the painted area is still 216.

Now, 27 smaller cubes means that the side of each cube has to be 1/3 of the original size, right? So each cube now has a side equal to 2. So the surface area of each of the small cubes is 6 x (2*2) = 24, so you have a total of 27*24 for the surface area, and the unpainted area must then be 27*24 - 216.

Answer 6

Well, if the whole cube is 6 by 6 by 6, and cut into 27 congruent cubes, you know that each of the smaller cubes is 2 by 2 by 2. Thus, the surface area of each of the smaller cubes is 2^2*6, or 24 sq units each.

To figure out how many of the small cubes are painted, and how many aren't, just picture the big cube that we have now. In this cube, it's three small cubes long, three small cubes wide, and three small cubes deep. If you were to imagine what isn't colored, there's the one cube in the very center of the large cube that doesn't have any paint on it. Which gets you the answer of part B, 1 cube times 24 sq units for the surface area, gets you 24 sq units.

Since one of the cubes ISN'T painted, the number of cubes that ARE painted is 27-1, or 26 cubes. 26 cubes times 24 sq units is 624 sq units, and the solution to part A.

Answer 7

SA = 6X6X6=216 cm^2
painted surface of the small cubes = 216 cm^2


Vol of small cube= 216/27 = 8 cm^3

=> SA = 2*2*6=24
=> SA of 27= 24 * 27 = 648
=> unpainted surface = 648-216 =432 cm^2

Answer 8

A) Call the painted area PA. PA = 6(36)=216 square units.

B) Call the total surface area of each little cube TA. TA = (27cubes)(24 sq. units surface area per cube, because the little cubes are 2x2x2) = 648 sq. units. Subtract PA from TA to get the answer:

648 - 216 = 432 sq. units

Answer 9

hmm this one's tricky.
divide 6 by 27 and u get 0.22222
square 0.22222 and u get 0.04938
what's tricky is that some cubes will have 2 surfaces painted while the inner ones will have none.
assuming each cube has one painted surface 0.04938 is the surface area of the painted region of the smaller cube.
now for the remaining five sides that are unpainted u multiply
0.04938 by five and get 0.2469 square units
im not sure. good luck.

Answer 10

a 6x6x6 cube cut into 27 cubes...so each cube will be 2x2x2
a) surface area is 6x (6x6)=216 ie the total area of the original cube.
b) 27x6x(2x2) - 6x6x6= 432 ie the total surface area of the small cubes - the area painted blue

Answer 11

8 cubes have three blue sides

12 cubes have two blue sides

6 cubes have 0ne blue side

1 cube has no blue sides

a) = 54 sq. units

b) = 108 sq. units

Consider looking at a Rubik's Cube and the answer will be very visual.