A right circular cylinder is contained within a sphere of radius 5 cm in such a way that the whole of the circumferences of both ends of the cylinder are in contact with the sphere. The diagram shows a planar cross section through the centre of the sphere and cylinder. Find, in cubic centimetres, the maximum possible volume of the cylinder. A $250 \pi$ B $500 \pi$ C $1000 \pi$ D $\frac { 250 \sqrt { 3 } } { 3 } \pi$ E $\frac { 500 \sqrt { 3 } } { 9 } \pi$ F $\frac { 1000 \sqrt { 3 } } { 9 } \pi$
& E & 12 & F
A right circular cylinder is contained within a sphere of radius 5 cm in such a way that the whole of the circumferences of both ends of the cylinder are in contact with the sphere.
The diagram shows a planar cross section through the centre of the sphere and cylinder.
Find, in cubic centimetres, the maximum possible volume of the cylinder.
A $250 \pi$
B $500 \pi$
C $1000 \pi$
D $\frac { 250 \sqrt { 3 } } { 3 } \pi$
E $\frac { 500 \sqrt { 3 } } { 9 } \pi$
F $\frac { 1000 \sqrt { 3 } } { 9 } \pi$