The diagram shows three solids. The base radius of the cone is 6 cm and the slant height is 12 cm.

The radius of the sphere is x cm and the radius of the hemisphere is y cm.

The total surface area of each solid is the same.

(i) Show that the total surface area of the cone is 108r cm2

.

[The curved surface area, A, of a cone with radius r and slant height l is A r = r l.]

[2]

(ii) Find the value of x and the value of y.

[The surface area, A, of a sphere with radius r is A r 4

2 = r .]