(a) 2 : 1
Let r be the radius of the cylindrical block, then height of the block = 2r.
Volume of the block = π(r2) (2r) = 2πr3
A sphere of maximum possible volume is carved out of the cylindrical block, so the radius of the sphere = r.
∴ Volume of sphere = \(\frac43\)πr3 = Volume of utilised wood
∴ Volume of wasted wood = 2πr3 – \(\frac43\)πr3 = \(\frac{2πr^3}{3}\)
∴ Required ratio = \(\frac43\)πr3 : \(\frac23\)πr3 = 2 : 1.