Respuesta :
Answer:
a) 5572.45 cubic inches
b) 2786.23 cubic inches
c) 8.7 inches
Step-by-step explanation:
We are given the following in the question:
Diameter of spherical balloon = 22 inch.
Thus,
Radius of spherical balloon, r = 11 inch
a) volume of the fully inflated balloon.
Volume of balloon = Volume of sphere
[tex]V=\dfrac{4}{3}\pi r^3[/tex]
Putting value, we get,
[tex]V = \dfrac{4}{3}\times 3.14\times (11)^3 = 5572.45\text{ cubic inches}[/tex]
The volume of fully inflated balloon is 5572.45 cubic inches.
b) volume of the half inflated balloon.
[tex]V' = \dfrac{1}{2}V\\\\V' = \dfrac{1}{2}\times 5572.45\\\\V' = 2786.225\approx 2786.23\text{ cubic inches}[/tex]
The volume of half inflated balloon is 2786.23 cubic inches.
c) Radius of half inflated balloons
[tex]V=\dfrac{4}{3}\pi r^3[/tex]
Putting values, we get
[tex]2786.23 =\dfrac{4}{3}\times 3.14\times r^3\\\\r^3 = \dfrac{2786.23\times 3}{4\times 3.14}\\\\r^3 = 665.5\\\Rightarrow r = 8.73\approx 8.7\text{ inches}[/tex]
Thus, the radius of half inflated balloon is 8.7 inches
