Cubes and Cuboids Flashcards

1
Q

How many faces are on a cube or cuboid?

A

6 faces

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2
Q

What’s the formula for the number of unit cubes in a cube?

A

(side)³

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3
Q

What’s the relationship between the length, breadth and height in a cube?

A

The length, breadth and height are all the same

NOTE: In a cuboid, the length, breadth, and height are all different values.

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4
Q

What’s the formula for the number of unit cubes in a cuboid?

A

l * b * h, where l is length, b is breadth, and h is height

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5
Q

What is the maximum number of faces on a cube or cuboid that you can see at any angle?

A

3 faces; there are 6 faces, 3 pairs of opposite faces, and you cannot see a pair of opposite faces at the same angle

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6
Q

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?

A

(n - 2)³

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7
Q

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?

A

6(n - 2)²

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8
Q

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?

A

12(n - 2)

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9
Q

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?

A

8

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10
Q

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

(a - 2)(b - 2)(c - 2)

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11
Q

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?

A

2[(a - 2)(b - 2) + (b - 2)(c - 2) + (a - 2)(c - 2)]

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12
Q

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?

A

4(a - 2) + 4(b - 2) + 4(c - 2) = 4(a + b + c -6)

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13
Q

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?

A

8

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14
Q

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?

A

(n - 2)² * 3 + 9 * (n - 2) + 7

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15
Q

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?

A

3(a + b + c - 6) + [(a - 2)(b - 2) + (b - 2)(c - 2) + (a - 2)(c - 2)] + 7

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