(a) Bowl is a hemisphere of radius5.6 cm; cylindrical tin is10 cm high. \(V_{\text{sphere}}=\frac43\pi r^3\).

(a(i)) Show the bowl volume rounds to368 cm³. [2]

(a(ii)) Soup from a completely full tin fills80% of the empty bowl. Find the tin radius. [4]

(b) A cone has radius1.75 cm and height6 cm. \(A_{\text{curved}}=\pi rl\).

(b(i)) Find its total surface area. [5]

(b(ii)(a)) Salt fills the cone to depth4.5 cm, its top parallel to the base. Show its volume is18.9 cm³ to1 decimal place. \(V=\frac13\pi r^2h\). [4]

(b(ii)(b)) Remove all salt at200 mm³/s. Find the time to empty, to the nearest second. [3]