Answer:
The volume of the shaded figure is 252π feet³ ⇒ 1st answer
Step-by-step explanation:
* Lets revise how to find the volume of the sphere
- The volume of any sphere is [tex]\frac{4}{3}\pi r^{3}[/tex], where
r is the radius of the sphere
- There is a large sphere of diameter 12 feet
- The diameter of the sphere is twice its radius
∵ The length of the diameter is 12 feet
∴ The length of the radius = [tex]\frac{1}{2}*12=6[/tex] feet
- There is a smaller sphere with a radius of 3 feet
- The smaller sphere is cut out of the center of the larger sphere
- The volume of the shaded part is the difference between the
volumes of the larger sphere and the smaller sphere
* Lets find the volume of each sphere
- The volume of the larger sphere:
V larger = [tex]\frac{4}{3}\pi (6)^{3}[/tex] = 288π feet³
- The volume of the smaller sphere:
V smaller = [tex]\frac{4}{3}\pi (3)^{3}[/tex] = 36π feet³
∴ The volume of the shaded figure = 288π - 36π = 252π feet³
* The volume of the shaded figure is 252π feet³
