Question 188907
A design on the surface of a balloon is 5 cm wide when the balloon holds 71 cm^3 of air.
 How much air does the balloon hold when the design is 10 cm wide?
:
Let r = radius then balloon has 71 cu/cm
{{{(4/3)pi*r^3}}} = 71
{{{pi*r^3}}} = {{{71 * 3/4}}}
{{{pi*r^3}}} = 53.25
r^3 = {{{53.25/pi}}}
r^3 = 16.95
r = 2.57 cm when the balloon holds 71 cu/cm
:
Find the surface area:
SA = 4*pi*2.57^2
SA = 83 sq/cm
:
To double the surface area so the design goes from 5 cm to 10 cm wide
Find r for double the surface area
4*pi*r^2  = 166 sq/cm
r = {{{sqrt(166/(4*pi))}}}
r = 3.63 cm
:
Find volume when r = 3.63
V = {{{(4/3)*pi*3.63^3}}}
V = 200.36 cu/cm