Quandaries
and Queries 

Who is asking: Other Level: Secondary Question: twenty cubic metres of air are pumped into a spherical hot air balloon with each given diameter: 1.0m; 2.0m; 3.0m; 4.0m; 5.0m;6.0m 

Hi, Lets do it with a diameter of 2 meters. By adding 20 cubic meters you are increasing the volume by 20 cubic meters. (Actually the volume will be a little less since the pressure inside the balloon will decrease the volume somewhat.) The volume of a sphere is given by
where r is the radius. Thus the volume of the sphere before increasing the volume is
Thus the new volume is
If the radius of this expanded sphere is R then
Solve for R and then the diameter is 2 R. Once you have the radius you can also find the surface area. Penny 

