Quandaries and Queries


Who is asking: Other
Level: Secondary

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.




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 = 4/3 134/3 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.



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