Simpler Holey Cube

Geometry Level 5

A cube of length 10 cm is drilled through the centre of three faces. If the cross-sectional area of the square drill bit is 6.25 cm 2 6.25 \text{ cm}^{2} , what is the volume of this shape in cubic centimetres?

For a harder problem, try The Holey Cube .


The answer is 843.75.

Steven Zheng by Steven Zheng , 26, China

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2 solutions

Ajay Nandugopal
Jan 25, 2015

volume of the remaining portion = vol of cube - ( 3 volume of cuboid -2 vol of smaller cube) side of smaller cube =2.5(formed at the center) dimensions of cuboid = (length=10,breadth=height=2.5) volume=10 10 10 -( 3 6.25 10 - 2 2.5 2.5*2.5) = 1000 -156.25=843.75

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Rwit Panda
Dec 7, 2015

The total volume of cube initially was 1000.

3 cuboids are cut, each with volume = 6.25*10 = 62.5

So volume of 3 of them is = 62.5*3 = 187.5

But, we need to remember that in adding volumes of 3 cuboids, volume of intersecting cube (6.25*2.5 = 15.625) has been included 3 times, i.e., 2 times extra.

So, remaining volume is 1000 - 187.5 + 2*15.625 = 843.75 :)

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