Respuesta :
28.75We are asked to determine the volume of a hemisphere of diameter 28 3/4 in.
A hemisphere is half a sphere therefore, its volume is half the volume of a sphere:
[tex]V=\frac{1}{2}(\frac{4\pi r^3}{3})=\frac{2\pi r^3}{3}[/tex]Where "r" is the radius. Since the radius is half the diameter we have that:
[tex]r=\frac{D}{2}=\frac{28\frac{3}{4}}{2}[/tex]We will convert the mixed fraction into a standard fraction using the following:
[tex]28\frac{3}{4}=28+\frac{3}{4}=28.75[/tex]Substituting in the formula for the radius:
[tex]r=\frac{28.75in}{2}=14.38in[/tex]Now, we substitute the value of the radius in the formula for the volume:
[tex]V=\frac{2\pi(14.38in)^3}{3}[/tex]Solving the operations:
[tex]V=6221.3in^3[/tex]Therefore, the volume is 6221.3 cubic inches.
