Calculate the total volume of all \(75\) metal cannon balls excavated.

The cannon balls are to be melted down to form a sculpture in the shape of a cone. The base radius of the cone is \(20{\text{ cm}}\).

Calculate the height of the cone, assuming that no metal is wasted.

\(75 \times \frac{4}{3}\pi  \times {5^3}\)     (M1)(M1)

Notes: Award (M1) for correctly substituted formula of a sphere. Award (M1) for multiplying their volume by \(75\). If \(r = 10\) is used, award (M0)(M1)(A1)(ft) for the answer 314000 cm³ .

\(39300{\text{ c}}{{\text{m}}^3}\) .     (A1)     (C3)

\(\frac{1}{3}\pi  \times {20^2} \times h = 39300\)     (M1)(M1)

Notes: Award (M1) for correctly substituted formula of a cone. Award (M1) for equating their volume to their answer to part (a).

\(h = 93.8{\text{ cm}}\)     (A1)(ft)     (C3)

Notes: Accept the exact value of \(93.75\) . Follow through from their part (a).

[3 marks]

As well as some candidates reading the diameter given as the radius, there was much confusion between the area and volume of a sphere and, although there was some recovery when multiplying by \(75\), two of the three marks were invariably lost. Recovery was possible in part (b) and many successful attempts were seen to calculate the height of the cone.

As well as some candidates reading the diameter given as the radius, there was much confusion between the area and volume of a sphere and, although there was some recovery when multiplying by \(75\), two of the three marks were invariably lost. Recovery was possible in part (b) and many successful attempts were seen to calculate the height of the cone.