Find the radius, \(r\), of the circular base of the cone.

Find the slant height, \(l\), of the cone.

Find the curved surface area of the cone.

\(100 = \frac{1}{3}\pi {r^2}(8)\)     (M1)

Note:     Award (M1) for correct substitution into volume of cone formula.

\(r = 3.45{\text{ (cm) }}\left( {3.45494 \ldots {\text{ (cm)}}} \right)\)     (A1)     (C2)

[2 marks]

\({l^2} = {8^2} + {(3.45494 \ldots )^2}\)     (M1)

Note:     Award (M1) for correct substitution into Pythagoras’ theorem.

\(l = 8.71{\text{ (cm) }}\left( {8.71416 \ldots {\text{ (cm)}}} \right)\)     (A1)(ft)     (C2)

Note:     Follow through from part (a).

[2 marks]

\(\pi  \times 3.45494 \ldots  \times 8.71416 \ldots \)     (M1)

Note:     Award (M1) for their correct substitutions into curved surface area of a cone formula.

\( = 94.6{\text{ c}}{{\text{m}}^2}{\text{ }}(94.5836 \ldots {\text{ c}}{{\text{m}}^2})\)     (A1)(ft)     (C2)

Note:     Follow through from parts (a) and (b). Accept \(94.4{\text{ c}}{{\text{m}}^2}\) from use of 3 sf values.

[2 marks]