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.
EC
Related Maths GCSE answers
All answers ▸The straight line L1 passes through the points with coordinates (4, 6) and (12, 2) The straight line L2 passes through the origin and has gradient -3. The lines L1 and L2 intersect at point P. Find the coordinates of P.
Find the value of 125^(2/3)
There are 10 boys and 20 girls in a class. The mean mark for the class is 60, the mean mark for the girls is 54. Work out the mean mark for the boys.
A right-angled triangle has a base of 5 cm, a height of 12 cm. Find the length of the hypotenuse.