Spheres, cylinders and cones

There are 32 NRICH Mathematical resources connected to Spheres, cylinders and cones

problem

Conical Bottle

Age

14 to 16

Challenge level

A right circular cone is filled with liquid to a depth of half its vertical height. The cone is inverted. How high up the vertical height of the cone will the liquid rise?

problem

In a Spin

Age

14 to 16

Challenge level

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

problem

Three Balls

Age

14 to 16

Challenge level

A circle has centre O and angle POR = angle QOR. Construct tangents at P and Q meeting at T. Draw a circle with diameter OT. Do P and Q lie inside, or on, or outside this circle?

problem

Ball Packing

Age

14 to 16

Challenge level

If a ball is rolled into the corner of a room how far is its centre from the corner?

problem

Two circles of equal size intersect and the centre of each circle is on the circumference of the other. What is the area of the intersection? Now imagine that the diagram represents two spheres of equal volume with the centre of each sphere on the surface of the other. What is the volume of intersection?