a snowman is made of three spherical snowballs with a diameters of 3 feet, 2 feet, and 1 foot. what is the total volume of the snowman?represent your answer in terns of pi

Answer:The total volume of the snowman is [tex]6\pi\ ft^{3}[/tex]Step-by-step explanation:we know thatThe volume of a sphere is equal to[tex]V=\frac{4}{3}\pi r^{3}[/tex]step 1Find the volume of the spherical snowball with a diameter of 3 feetFind the radius[tex]r=3/2=1.5\ ft[/tex] ----> the radius is half the diametersubstitute[tex]V=\frac{4}{3}\pi (1.5)^{3}[/tex][tex]V1=\frac{9}{2}\pi\ ft^{3}[/tex]step 2Find the volume of the spherical snowball with a diameter of 2 feetFind the radius[tex]r=2/2=1\ ft[/tex] ----> the radius is half the diametersubstitute[tex]V=\frac{4}{3}\pi (1)^{3}[/tex][tex]V2=\frac{4}{3}\pi\ ft^{3}[/tex]step 3Find the volume of the spherical snowball with a diameter of 1 feetFind the radius[tex]r=1/2=0.5\ ft[/tex] ----> the radius is half the diametersubstitute[tex]V=\frac{4}{3}\pi (0.5)^{3}[/tex][tex]V3=\frac{1}{6}\pi\ ft^{3}[/tex]step 4Find the total volume[tex]V=V1+V2+V3[/tex]substitute the values[tex]V=\frac{9}{2}\pi+\frac{4}{3}\pi+\frac{1}{6}\pi=\frac{27+8+1}{6}\pi=6\pi\ ft^{3}[/tex]