A 10cm long cylindrical hole is drilled straight through the centre of a solid sphere.

What is the volume of the remaining part of the sphere?

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524 cm^{3} to three significant figures.

One approach is to let the sphere have a radius, say R, an then do some calculations using the formulas for the volumes of a sphere, cylinder and a spherical cap. A much quicker method however requires a little creative thinking. As the puzzle has been presented on this website you can assume that there is a solution. As the size of the sphere is not given it is reasonable to assume the solution is independent of any sphere dimensions. In that case you can consider the limiting case, one in which the radius of the sphere is 5cm and the radius of the spherical hole is zero. The remaining volume would then be the total volume of the sphere which equals 524 cubic centimetres to three significant figures.

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