A spinning top is made from two pieces glued together, a hemisphere and a cone.

(1) If the radius of the circular surface where the pieces are glued together is 3 cm, and the slant height of the cone is 5 cm, work out the total volume and surface area of the spinning top (top A).

(2) If each top is packed in a box measuring 6.5 cm by 6.5 cm by 7.5 cm how many tops will fit into a packing case measuring 55 cm by 55 cm by 55 cm?

(3) Two more tops are made the same way with the circular surface where the pieces are glued together having radius 3 cm. For top B the volume of the hemisphere is equal to the volume of the cone and for top C the surface area of the hemisphere is the same as the surface area of the cone. In each case, for top B and for top C, find h cm the height of the cone.

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