(a(i)) Find the external curved surface area of a cylinder of radius 8 m and height 19 m. [2]

(a(ii)) Painting costs \$0.85 per m². Find the cost of painting this curved surface. [2]

A solid metal sphere of radius 6 cm is melted into a solid cone of radius 8 cm and height h cm. \(V_{\rm sphere}=\frac43\pi r^3,\quad V_{\rm cone}=\frac13\pi r^2h\).

(b(i)) Show that h=13.5. [2]

(b(ii)) Find the cone’s slant height. [2]

(b(iii)) Find its curved surface area, using \(A=\pi rl\). [1]

(c) Similar cones have total surface areas 80 cm² and 180 cm². The smaller volume is 168 cm³. Find the larger volume. [3]

(d) The pyramid has square base ABCD, diagonal DB=8 cm and vertical height PX=5 cm. X is the base centre. Find the angle between PB and the base. [3]