A cone of maximum volume is carved out of a block of wood of size 20 cm × 10 cm × 10 cm. Find the volume of the cone carved out, correct to one decimal place.

From a solid wooden cylinder of height 28 cm and diameter 6 cm, two conical cavities are hollowed out. The diameters of the cones are also of 6 cm and height 10.5 cm. Find the volume of the remaining solid.

The volume of a sphere is 228 π cm³. Calculate its radius and hence its surface area to nearest cm².

The curved surface area of a sphere is 2826 cm². Calculate its radius and hence its volume .

(Take π = 3.14)