Answer:
Volume of hemisphere: 10,851.84
Volume of cone: 9,043.2
Total volume: 19,895.04
Time to fill the balloon: 284 minutes
Step-by-step explanation:
To find the time, calculate the volume divide it by the rate 70 cubic feet per minute.
The volume of a cone is found using the volume formula for a cone [tex]V=\frac{1}{3}\pi r^2h[/tex].
Substitute h=60 and r = 12.
[tex]V = \frac{1}{3}\pi r^2h\\V = \frac{1}{3}\pi (12^2)(60)\\V=\frac{1}{3}\pi *144*60\\V = \frac{8640}{3}\pi \\V= 2880\pi = 9,043.2[/tex]
The volume of a hemisphere is half of the volume of a sphere [tex]V=\frac{4}{3}\pi r^3[/tex]. Substitute r=12.
[tex]V=\frac{4}{3}\pi r^3\\V=\frac{4}{3}\pi 12^3\\V=\frac{4}{3}\pi *1728\\V=\frac{4*1728}{3}\pi\\ V=6912\pi = 21,703.68 [/tex]
However the hemisphere is half this so it is [tex]10,851.84[/tex].
Together the volume is 10,851.84 + 9,043.2 = 19,895.04
Divide this by 70 and the float fills up in 284 minutes.
