In the given figure, a solid cone is kept inverted in a closed cylindrical container such that the height of cone = height of cylinder = h, radius of cone = radius of cylinder = r and slant height of cone = l. If the remaining of cylinder is completely filled with water, the wetted surface area of the whole body is :

1. 2πrh + πr² + πrl

2. 2πrh + πrl

3. 2πrh + 2πr² + πrl

4. 2πrh - πr² + πrl

A buoy is made in the form of a hemisphere surmounted by a right cone whose circular base coincides with the plane surface of the hemisphere. The radius of the base of the cone is 3.5 metres and its volume is two-third of the hemisphere. Calculate the height of the cone and the surface area of the buoy, correct to two places of decimal.

From a rectangular solid of metal 42 cm by 30 cm by 20 cm, a conical cavity of diameter 14 cm and depth 24 cm is drilled out. Find:

(i) the surface area of the remaining solid

(ii) the volume of remaining solid

(iii) the weight of the material drilled out if it weighs 7 gm per cm³.