Respuesta :
The formula for getting the volume of a hemisphere is this:
[tex]V=\frac{2\pi r^3}{3}[/tex]From this formula, we can solve for the radius then, the diameter of the hemisphere.
Let's plug into the formula above the given volume of the hemisphere.
[tex]458ft^3=\frac{2\pi r^3}{3}[/tex]Let's now solve for the radius.
1. Cross multiply both sides of the equation.
[tex]458ft^3\times3=2\pi r^3[/tex][tex]1,374ft^3=2\pi r^3[/tex]2. Divide both sides of the equation by 2π.
[tex]\frac{1,374ft^3}{2\pi}=\frac{2\pi r^3}{2\pi}[/tex][tex]218.67889ft^3=r^3[/tex]3. Get the cube root on both sides of the equation.
[tex]\sqrt[3]{218.67889ft^3}=\sqrt[3]{r^3}\Rightarrow6.0247ft=r[/tex]Therefore, the radius of the hemisphere is approximately 6.0247 ft.
Since the diameter is twice the radius, then the diameter is:
[tex]D=6.0247ft\times2=12.0494ft[/tex]Therefore, the diameter of the hemisphere is approximately 12.0 ft.
