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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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Concrete Calculation

The builders have dug a hole in the ground to be filled with concrete for the foundations of our garage. How many cubic metres of ready-mix concrete should the builders order to fill this hole to make the concrete raft for the foundations?

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In a Spin

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

Efficient Cutting

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

The width of the A4 sheet could determine the circumference of the base of the cylinder. Then the diameter of the base restricts how high the cylinder can be - can you work out the dimensions of this cylinder?

The length of the A4 sheet could determine the circumference of the base of the cylinder.

The width of the A4 sheet could determine the height of the cylinder.

The length of the A4 sheet could determine the height of the cylinder.