Answer:
375.4 ft
Step-by-step explanation:
Volume of sphere is given by [tex](4\pi r^3)/3[/tex]
where is the radius
since hemisphere is half of sphere, its volume is half of volume of sphere
Volume of hemisphere is given by [tex](1/2)(4\pi r^3)/3 = (2\pi r^3)/3[/tex]
Given volume of sphere is 73802 ft^3.
equating this value with formula for Volume of hemisphere, we have
[tex](2\pi r^3)/3 = 73802 ft^3 \\=>\pi r^3 = 3/2( 73802) ft^3\\=>22/7 r^3 = 110,703 ft^3\\=> r^3 = 7/22(110,703 )ft^3\\=> r^3 = 35223.6818\\=> r = \sqrt{35223.6818}\\=> r = 187.679[/tex]
Thus, radius of hemisphere is 187.679 ft
we know that diameter is twice of radius
therefore
diameter of hemisphere = 2*187.679 ft = 375.358 ft.
diameter of hemisphere to the nearest tenth of a foot= 375.4 ft
