(a) Similar triangles ABC and PQR have corresponding sides8 cm and12 cm. ABC has area16 cm².

(a(i)) Find the area of PQR. [2]

(a(ii)) The triangles are cross-sections of similar prisms. The smaller prism has volume320 cm³. Find the length of the larger prism. [3]

(b) A cylinder of radius6 cm and height h has the same volume as a sphere of radius4.5 cm. Find h. \(V_{\rm sphere}=\frac43\pi r^3\). [3]

(c) A solid cube of side20 cm is melted into40 solid spheres of radius r. Find r. [3]

(d) A cylinder has radius x and height7x/2. Its total surface area equals the surface area of a sphere of radius R. Find R in terms of x. \(A_{\rm sphere}=4\pi R^2\). [3]