Answer : The volume of shaded figure is, [tex]791.28ft^3[/tex]
Step-by-step explanation :
First we have to calculate the volume of small sphere.
Formula used :
[tex]V_1=\frac{4}{3}\pi r^3[/tex]
where,
[tex]V_1[/tex] = volume of small sphere
r = radius of small sphere = 3 ft
Now put all the given values in the above formula, we get:
[tex]V_1=\frac{4}{3}\times 3.14\times (3)^3[/tex]
[tex]V_1=113.04ft^3[/tex]
Now we have to calculate the volume of larger sphere.
Formula used :
[tex]V_2=\frac{4}{3}\pi r^3[/tex]
where,
[tex]V_2[/tex] = volume of larger sphere
r = radius of larger sphere = [tex]\frac{\Diameter}{2}=\frac{12ft}{2}=6ft[/tex]
Now put all the given values in the above formula, we get:
[tex]V_2=\frac{4}{3}\times 3.14\times (6)^3[/tex]
[tex]V_2=904.32ft^3[/tex]
Now we have to calculate the volume of shaded figure.
Volume of shaded figure = Volume of larger sphere - Volume of smaller sphere
Volume of shaded figure = [tex]904.32ft^3-113.04ft^3[/tex]
Volume of shaded figure = [tex]791.28ft^3[/tex]
Therefore, the volume of shaded figure is, [tex]791.28ft^3[/tex]
