A cylindrical can whose base is horizontal and of radius 3.5 cm contains sufficient water so that when a sphere is placed in the can, the water just covers the sphere. Given that the sphere just fits into the can, calculate :

(i) the total surface area of the can in contact with water when the sphere is in it.

(ii) the depth of the water in the can before the sphere was put into the can. Given your answer as proper fractions.

If two cylinders of the same lateral surface have their radii in the ratio 4 : 9, then the ratio of their heights is

1. 2 : 3

2. 3 : 2

3. 4 : 9

4. 9 : 4

The total surface area of a cone whose radius is $\dfrac{r}{2}$ and slant height 2l is

1. 2πr(l + r)

2. $πr \Big(l + \dfrac{r}{4}\Big)$

3. πr(l + r)

4. 2πrl

If the diameter of the base of cone is 10 cm and its height is 12 cm, then its curved surface area is

1. 60π cm²

2. 65π cm²

3. 90π cm²

4. 120π cm²