A design on the surface of a balloon is 5 cm wide when the balloon holds 71 cm of air. How much air does the balloon hold when the design is 10 cm wide? Explain the method you use to find the amount of air. |

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natasza
Jun 25, 2014

#2**+10 **

We have

V = (4/3)*pi*r^3

71 = (4/3) *pi * r^3 Solving for r , we have

71(3/4)/pi = r^3 Taking the cube root of both sides, we have

r = 2.5687583235794156 And if the design is now 10cm wide, the dimensions of the balloon must have doubled....so doubling the radius, we have 2 * 2.5687583235794156 = 5.1375166471588312

So

V = (4/3)*pi * (5.1375166471588312)*3 = 567.99999cm^3 or 568cm^3

Obviously, Melody's path to the answer is more elegant than mine !!!

CPhill
Jun 25, 2014

#1**+10 **

I think if a length dimension is 2*original then the volume is 2cubed=8 times original.

$$71*8=568cm^3$$

I'm another mathematician will look at my answer.

Melody
Jun 25, 2014

#2**+10 **

Best Answer

We have

V = (4/3)*pi*r^3

71 = (4/3) *pi * r^3 Solving for r , we have

71(3/4)/pi = r^3 Taking the cube root of both sides, we have

r = 2.5687583235794156 And if the design is now 10cm wide, the dimensions of the balloon must have doubled....so doubling the radius, we have 2 * 2.5687583235794156 = 5.1375166471588312

So

V = (4/3)*pi * (5.1375166471588312)*3 = 567.99999cm^3 or 568cm^3

Obviously, Melody's path to the answer is more elegant than mine !!!

CPhill
Jun 25, 2014