Question

A cube is painted blue on two adjacent surfaces and black on the surfaces opposite to blue surfaces and green on the remaining faces .Now the cube is cut into 216 smaller cubes of equal size. How many of the pieces will have black colour on them?

Answer 1

Answer:

72

Step-by-step explanation:

Answer 2

ANSWER:

A cube is painted blue on two adjacent surfaces. 66 cubes have black paint.

SOLUTION:

Given, a cube is painted blue on two adjacent surfaces  

And black on the surfaces opposite to blue surfaces and green on the remaining faces .

Now the cube is cut into 216 smaller cubes of equal size.

We need to find how many of the pieces will have black colour on them?

Let the side length of original cube be x. Then volume of original cube = $x^{3}$

And let the side length of each small cube be y. then, volume of small cube = $y^{3}$

Now, volume of original cube = number of small cubes x volume of small cube.

$\begin{array}{l}{x^{3}=216 x y^{3}} \\\\ {x^{3}=6^{3}y^{3}} \\\\ {x^{3}=(6 y)^{3}} \\\\ {x=6 y}\end{array}$

Which means that, each side edge of original cube is cut into 6 smaller cubes.

Which in turn, makes 6 x 6 cubes for one surface.

We have two surfaces painted with black, then total cubes painted in black are 2 x 36 = 72 cubes.

Now, black is painted on adjacent surfaces, so 6 cubes are common to both surfaces, which means we have counted those 6 cubes two times.

So, number of cubes with black paint are 72 – 6 = 66 cubes.

Hence, 66 cubes have black paint.