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The original large cube with 16 small cubes along each edge would required 16 x 16 x 16 = 4,096 small cubes.
Removing the outside layer would leave a large cube now with 14 small cubes along each edge (which requires 14 x 14 x 14 = 2,744 small cubes).
It isn't 15 small cubes because you're removing both ends of an edge.
Therefore you have removed 4,096  2,744 = 1,352 small cubes.
Puzzle 146
Using the clues below can you find 8 four letter words.
Once you have placed the words into the correct order you will find that each word is different from the previous word by only one letter.
For example, FARE may be followed by FIRE, etc.
An imperfection
Additional items
Insufficiently heated
A female equine
Hotter than temperate
An article of commerce
The middle of an apple
Insulated electrical wire
Insufficiently heated = cold
Insulated electrical wire = cord
The middle of an apple = core
Additional items = more
A female equine = mare
An article of commerce = ware
An imperfection = wart
Hotter than temperate = warm
The larger circle has diameter = 4, therefore the radius is 2, and the area is π x 2^{2} = 4π.
The smaller circle has diameter = 2, therefore the radius is 1, and the area is π x 1^{2} = π.
Therefore the shaded area is 4π  π = 3π ≈ 9.42.
Circle
The area of a circle is π x Radius^{2}.
The circle with diameter 3.1 has a radius of 1.55 and an area of π x 1.55^{2} = 7.55.
The circle with diameter 3.5 has a radius of 1.75 and an area of π x 1.75^{2} = 9.62 (** closest match).
The circle with diameter 3.9 has a radius of 1.95 and an area of π x 1.95^{2} = 11.95.
Square
The area of a square is Side x Side.
The square with side 3.1 has an area of 3.1 x 3.1 = 9.61 (** closest match).
The square with side 3.5 has an area of 3.5 x 3.5 = 12.25.
The square with side 3.9 has an area of 3.9 x 3.9 = 15.21.
Triangle
The area of a triangle is ½ x Base x Height. Using Pythagoras' theorem it can be shown that the area of an equilateral triangle is Sqrt(3) x Base^{2} ÷ 4.
The triangle with side 3.9 has an area of Sqrt(3) x 3.9 x 3.9 ÷ 4 = 6.59.
The triangle with side 4.3 has an area of Sqrt(3) x 4.3 x 4.3 ÷ 4 = 8.01.
The triangle with side 4.7 has an area of Sqrt(3) x 4.7 x 4.7 ÷ 4 = 9.57 (** closest match).
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