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Cones and Spheres

Age 14 to 16 Short
Challenge Level

We need to find the volume of the cone and the volume of metal needed for each sphere.

The volume of a cone is given by $\frac{1}{3}\pi r^2h$, where $r$ is the radius and $h$ is the height. So the volume of the cone, in cubic centimetres, is $\frac{1}{3}\pi \times 6^2\times20=240\pi$.

The volume of a sphere is given by $\frac{4}{3}\pi r^3$. The radius of each of the spheres is 3 cm, so the volume of each of the spheres, in cubic centimetres, is $\frac{4}{3}\pi\times3^3=4\times 9\pi=36\pi$.

$240\div36=6.\dot6=6\frac{2}{3}$, so 6 spheres can be made.
You can find more short problems, arranged by curriculum topic, in our short problems collection.