Three solid metallic spheres of radii 1 cm,6 cm and 8 cm, respectively, are melted and recast into a single solid sphere. The radius of the new sphere so formed is:

A solid sphere is placed inside a cube such that it touches all six faces. What percentage of the cube's volume is not occupied by the sphere?

If the radius of a sphere is increased to twice its original size, what is the ratio of the new surface area to the original surface area, as well as the proportion of the new volume to the original volume?

A metal sphere having a radius of 10 centimeters is melted down and molded into 8 identical smaller solid spheres. What is the ratio of the surface area of the original sphere to the total surface area of all 8 smaller spheres?

What will be the surface area of the sphere having 5.4 cm radius?

Find the volume of the sphere whose diameter is 30 cm. (Use π = 3.14).

Find the surface area of a sphere whose diameter is equal to 14 cm.

The curved surface area of a sphere is 9856 cm², find its diameter in m.