The surface area of a solid metallic sphere is 1256 cm². It is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate

(i) the radius of the solid sphere.

(ii) the number of cones recast. (Use π = 3.14).

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.

The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. The ratio of their volumes is

1. 10 : 17

2. 20 : 27

3. 17 : 27

4. 20 : 37

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