We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

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. |

Thank You All For All the Help! Couldnt do It Without You! :D

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