Quandaries and Queries Who is asking: Other Level: Secondary Question: my friend's teacher gave her a math question and she asked me for some help with it but we can't get it. here it is: 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 a)calculate the new diameter, new suface area, and new volume of each balloon. 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 volume = 4/3 r3 where r is the radius. Thus the volume of the sphere before increasing the volume is volume = 4/3 13 = 4/3 cubic meters. Thus the new volume is 20 + 4/3 cubic meters. If the radius of this expanded sphere is R then volume = 4/3 R3 = 20 + 4/3 cubic meters Solve for R and then the diameter is 2 R. Once you have the radius you can also find the surface area. Penny Go to Math Central