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Qqq..cubed

It is known that the area of the largest equilateral triangular section of a cube is 140sq cm. What is the side length of the cube? The distances between the centres of two adjacent faces of another cube is 8cms. What is the side length of this cube? Another cube has an edge length of 12cm. At each vertex a tetrahedron with three mutually perpendicular edges of length 4cm is sliced away. What is the surface area and volume of the remaining solid?

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In a Spin

What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?

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Mouhefanggai

Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.

Concrete Calculation

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

You might like to imagine cutting the mound of earth into a cuboid, four prisms and four little pyramids in the corners. You'll need the formula (Area of base x Height)/3 for the volume of a pyramid.