SOLUTION: Good evening, i would like to ask you this three problems, i am not sure that i work out the answers. Please, help in those 1) A solid cube of side 6 is first painted pink and

Question 53409: Good evening, i would like to ask you this three problems, i am not sure that i work out the answers. Please, help in those

1) A solid cube of side 6 is first painted pink and then cut into smaller cubes of side 2. How many of the smaller cubes have paint on exactly 2 sides?
2) A regular hexagon is inscribed in a circle o radius R cms. What is the perimeter of the regular hexagon?
3) A 4cm cube is cut into 1cm cubes. What is the percentage increase in the surface area after such cutting?
From yours poor students
babynarah and modi
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1) A solid cube of side 6 is first painted pink and then cut into smaller cubes of side 2. How many of the smaller cubes have paint on exactly 2 sides?
Before cutting the cube is 6^3 cb. units = 216 cu units
The smaller cubes are 2^3 units or 8 cu units
Dividing 216 by 8 you get 27 small cubes.
How many of them have paint on exactly two sides?
There are four on each edge; so there are 4*6=24 with exactly
two pink sides.
-------------
2) A regular hexagon is inscribed in a circle of radius R cms. What is the perimeter of the regular hexagon?
Draw the picture of the hexagon.
Draw the 6 radii--one to each of the six vertices.
Each of the triangles formed is an equilateral triangle.
So all sides of each triagle are length 6.
So the perimeter of the hexagon is 6*6= 36 cm
3) A 4cm cube is cut into 1cm cubes. What is the percentage increase in the surface area after such cutting?
The surface area of the original cube is 6*4^2=96 cm sq.
Each of the 1cm cubes has a surface area of 6*1^2=6 cm sq.
There are 4^3=64 small cubes
The total surface area of the small cubes is 64*6=384 cm sq.
The increase in surface area is 384-96= 288 sq cm.
The % increase in surface area is 288/96=300%
Cheers,
Stan H.

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