a wooden cube 9*9*9 has three square holes drilled through it each of which forms a 3*3*9 tunnel through the centre of opposite faces.what is the total surface area of exposed wood
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a wooden cube 9*9*9 has three square holes drilled through it each of which forms a 3*3*9 tunnel through the centre of opposite faces.what is the total surface area of exposed wood
My "brain cells that handle 3D" are weak, few, and far apart.Quote:
Originally Posted by prasum
But here's what I'd do:
1: buy a perfect cube of soft cheese (on sale)
2: turn the 9*9*9 and 3*3*9 to 3*3*3 and 1*1*3
3: "line" the surfaces so that each looks like a "X and O" grid
4: going top to bottom and using appropriate kitchen knife,
remove the vertical 1*3 at center; so three 1*1's have been removed
5: perform similar surgery both ways horizontally; here one must remember
that only two 1*1's are removed for each (the center one is gone from step 4),
so four 1*1's have been removed
a = surface area of initial cube: 6 * 9 = 54
b = "removed area"; a 1*1 from each surface: 6 * 1 = 6
c = "added area"; that's 4 surfaces of six 1*1's: 6 * 4 = 24
So exposed area = a - b + c = 72
Now translate that to a 9*9*9.
Well, hope that helps a bit...
1. Draw a sketch.Quote:
Originally Posted by prasum
2. The surface of the original cube:
3. At each face is missing a square:
4. At each face you find 4 squares which form the walls of the holes:
5. Therefore the complete surface area is:
Or...
the outside surface area is the area of 8 squares on all 6 faces.
the internal surface area is 4 squares on each of the 6 walls.