Answer:
The volume of the toy is [tex]V=5.23\ ft^3[/tex]
Step-by-step explanation:
step 1
Find the volume of the hemisphere
The volume of the hemisphere is given by the formula
[tex]V=\frac{2}{3}\pi r^{3}[/tex]
In this problem, the wide of the toy is equal to the diameter of the hemisphere
so
[tex]D=2\ ft[/tex]
[tex]r=2/2=1\ ft[/tex] ----> the radius is half the diameter
substitute
[tex]V=\frac{2}{3} \pi (1)^{3}=\frac{2}{3} \pi\ ft^3[/tex]
step 2
Find the volume of the cone
The volume of the cone is given by
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]
we know that
The radius of the cone is the same that the radius of the hemisphere
so
[tex]r=1\ ft[/tex]
The height of the cone is equal to subtract the radius of the hemisphere from the height of the toy
[tex]h=4-1=3\ ft[/tex]
substitute the given values
[tex]V=\frac{1}{3}\pi (1)^{2}(3)=\pi\ ft^3[/tex]
step 3
Find the volume of the toy
we know that
The volume of the toy, is equal to the volume of the cone plus the volume of the hemisphere.
so
[tex]V=(\frac{2}{3} \pi+\pi)\ ft^3[/tex]
[tex]V=(\frac{5}{3}\pi)\ ft^3[/tex]
assume
[tex]\pi=3.14[/tex]
[tex]V=\frac{5}{3}(3.14)=5.23\ ft^3[/tex]
