1.a sphere with a radius of three units
By definition, the volume of a sphere is:
[tex]V = ( \frac{4}{3} ) (\pi) (r ^ 3)
[/tex]
Substituting values we have:
[tex]V=(\frac{4}{3})(\pi)(3^3)[/tex]
Rewriting we have:
[tex]V = (4) (\pi) (3 ^ 2)
V = (4) (\pi) (9)
V = 36\pi[/tex]
2.a cone with a diameter of twelve units and a height of three units
By definition, the volume of a cone is given by:
[tex]V = \frac{1}{3} (\pi) (r ^ 2) (h)
[/tex]
Substituting values we have:
[tex]V = \frac{1}{3} (\pi) ((\frac{12}{2}) ^ 2) (3)
[/tex]
Rewriting we have:
[tex]V = (\pi) (6 ^ 2)
V = 36\pi[/tex]
