A cube with an edge length of 4 inches is painted on all of its sides. Then the cube is cut into 64 cubes with an edge length of
1 inch. What percent of the total surface area is painted? Explain.
1 answer:
Please refer to the diagrams to understand these answers:
CUBE (1):
Paint on cube (1) contains 3.125% of the paint.
CUBE (2):
Paint on cube (2) contains 2.083% of the paint.
CUBE (3):
Paint on cube (3) contains 1.042% of the paint.
CUBE (4):
Contains 0% of the paint.
-----------------
There would be four different types of cubes which would contain different amounts of paint.
Some cubes in fact would have no paint (cube (4)). Now we can check if our results are correct by counting how many cube (1)'s, cube (2)'s, cube (3)'s and cube (4)'s there are...
Cube (1) x 8 + Cube (2) x 24 + cube (3) x 24 + cube (4) x 8
= 3.125% x 8 + 2.083% x 24 + 1.042% x 24 + 0% x 8
= 1
= 100%
CUBE (1):
Paint on cube (1) contains 3.125% of the paint.
CUBE (2):
Paint on cube (2) contains 2.083% of the paint.
CUBE (3):
Paint on cube (3) contains 1.042% of the paint.
CUBE (4):
Contains 0% of the paint.
-----------------
There would be four different types of cubes which would contain different amounts of paint.
Some cubes in fact would have no paint (cube (4)). Now we can check if our results are correct by counting how many cube (1)'s, cube (2)'s, cube (3)'s and cube (4)'s there are...
Cube (1) x 8 + Cube (2) x 24 + cube (3) x 24 + cube (4) x 8
= 3.125% x 8 + 2.083% x 24 + 1.042% x 24 + 0% x 8
= 1
= 100%
You might be interested in
Answer:
It is given that the volume of a cone = cubic units
Volume of cone with radius 'r' and height 'h' =
Equating the given volumes, we get
=
It is given that the height is 'x' units.
Therefore,
Therefore, r = 3x
So, the expression '3x' represents the radius of the cone's base in units.