Answer:
C. [tex]504\pi\text{ inches}^3[/tex]
Step-by-step explanation:
We have been given that a figure is a cylinder with a radius of 6 inches and a height of 10 inches. On top of the cylinder is a hemisphere with a radius of 6 inches.
The volume of our given figure will be equal to volume of cylinder plus volume of hemisphere.
[tex]\text{Volume of cylinder}=\pi r^2h[/tex], where,
r = Radius of cylinder,
h = height cylinder.
Upon substituting our given values in above formula we will get,
[tex]\text{Volume of cylinder}=\pi\text{(6 inch)}^2*\text{ 10 inches}[/tex]
[tex]\text{Volume of cylinder}=\pi*36\text{ inch}^2*\text{ 10 inches}[/tex]
[tex]\text{Volume of cylinder}=360\pi\text{ inch}3[/tex]
Now let us find the volume oh hemisphere part of our figure using formula,
[tex]\text{Volume of hemisphere}=\frac{2}{3}\pi r^3[/tex]
[tex]\text{Volume of hemisphere}=\frac{2}{3}\pi*\text{ 6 inches}^3[/tex]
[tex]\text{Volume of hemisphere}=\frac{2}{3}\pi*216\text{ inches}^3[/tex]
[tex]\text{Volume of hemisphere}=\pi*2*72\text{ inches}^3[/tex]
[tex]\text{Volume of hemisphere}=144\pi\text{ inches}^3[/tex]
[tex]\text{Volume of the figure}=\text{Volume of cylinder + Volume of hemisphere}[/tex]
[tex]\text{Volume of the figure}=360\pi\text{ inch}3+144\pi\text{ inches}^3[/tex]
[tex]\text{Volume of the figure}=504\pi\text{ inches}^3[/tex]
Therefore, the volume of our given figure is [tex]504\pi\text{ inches}^3[/tex] and option C is the correct choice.
