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