Answer:
Volume of Fully-inflated balloon: 17148.58 inches^3
Volume of half-inflated balloon: 8574.29 inches^3
Radius of half-inflated balloon: 12.7 inches
Step-by-step explanation:
Given
Diameter of inflated balloon=d=32 inches
As we have to use the radius of the balloon to calculate the volume then,
r=d/2
r=32/2
r=16 inches
Then balloon can be sphere when it has gas in it.
Volume of fully-inflated balloon:
Vhf=4/3 πr^3
=4/3*3.14*(16)^3
=12.56/3*4096
=51445.76/3
=17148.58 inches^3
Volume of Half-Inflated balloon:
As there will be half of the gas left, so the volume of half-inflated balloon will be the half of fully-inflated balloons volume.
Vh=Vf/2
=17148.58/2
=8574.29 inches^3
Radius of Half-inflated balloon:
As we know the volume of half inflated balloon, we will use the formula for volume to calculate the radius.
Vh=4/3 πr^3
8574.29=4/3*3.14*r^3
8574.29*3/4*1/3.14=r^3
r^3=2047.999
∛r= ∛2047.999
So,
r=12.69 ≈12.7 inches
