Cubes and Cuboids Flashcards
How many faces are on a cube or cuboid?
6 faces
What’s the formula for the number of unit cubes in a cube?
(side)³
What’s the relationship between the length, breadth and height in a cube?
The length, breadth and height are all the same
NOTE: In a cuboid, the length, breadth, and height are all different values.
What’s the formula for the number of unit cubes in a cuboid?
l * b * h, where l is length, b is breadth, and h is height
What is the maximum number of faces on a cube or cuboid that you can see at any angle?
3 faces; there are 6 faces, 3 pairs of opposite faces, and you cannot see a pair of opposite faces at the same angle
For a cube of side n x n x n painted on all sides which is uniformly cut into smaller cubes of dimension 1 x 1 x 1, what is the formula for the number of cubes with none of the sides painted?
(n - 2)³
For a cube of side n x n x n painted on all sides which is uniformly cut into smaller cubes of dimension 1 x 1 x 1, what is the formula for the number of cubes with only 1 side painted?
6(n - 2)²
For a cube of side n x n x n painted on all sides which is uniformly cut into smaller cubes of dimension 1 x 1 x 1, what is the formula for the number of cubes with 2 sides painted?
12(n - 2)
For a cube of side n x n x n painted on all sides which is uniformly cut into smaller cubes of dimension 1 x 1 x 1, how many cubes have 3 sides painted?
8
For a cuboid of dimension a x b x c painted on all sides which is cut into smaller cubes of dimension 1 x 1 x 1, what is the formula for the number of cubes with none of the sides painted?
(a - 2)(b - 2)(c - 2)
For a cuboid of dimension a x b x c painted on all sides which is cut into smaller cubes of dimension 1 x 1 x 1, what is the formula for the number of cubes with only 1 side painted?
2[(a - 2)(b - 2) + (b - 2)(c - 2) + (a - 2)(c - 2)]
For a cuboid of dimension a x b x c painted on all sides which is cut into smaller cubes of dimension 1 x 1 x 1, what is the formula for the number of cubes with 2 sides painted?
4(a - 2) + 4(b - 2) + 4(c - 2) = 4(a + b + c -6)
For a cuboid of dimension a x b x c painted on all sides which is cut into smaller cubes of dimension 1 x 1 x 1, how many cubes have 3 sides painted?
8
What is the formula for the maximum number of unit cubes you can see from any angle, for a cube with sides n x n x n?
(n - 2)² * 3 + 9 * (n - 2) + 7
What is the formula for the maximum number of unit cubes you can see from any angle, for a cuboid with sides a x b x c?
3(a + b + c - 6) + [(a - 2)(b - 2) + (b - 2)(c - 2) + (a - 2)(c - 2)] + 7