A hemisphere is placed on top of an upside down cone. The cone has height 9cm and the hemisphere has radius 3cm. The total volume of this composite solid is x cm^3. Calculate the value of x, leaving your answer in terms of π.

To work out the total volume of the composite solid, we need the volumes of both the cone and the hemisphere. GCSE Maths students are expected to know these respective formulae; volume of a sphere = ⁴/₃πr³ and volume of a cone = ¹/₃πr²h.
Hence, the volume of the hemisphere is ⁴/₃ × π × 3³ × ¹/₂ (being careful to half the volume that the full sphere would be) = 18π and the volume of the cone is ¹/₃ × π × 3² × 9 = 27π.
Therefore, the total volume of the solid and the value of x is 18π + 27π = 45π.