In this question, we have a composite figure. We can figure out that the composite figure is half of a sphere with a diameter of 12 inches and a cylinder with a height of 13 inches and a base with the same diameter.
Then, we have to calculate the volume of the sphere:
The radius of the sphere and the cylinder is 12/2 = 6 inches.
[tex]V_{\text{sphere}}=\frac{4}{3}\cdot\pi\cdot r^3=\frac{4}{3}\cdot\pi\cdot6^3=904.78in^3[/tex]
Since we have half of the sphere, we need to divide the previous result by 2:
[tex]V_{\text{semisphere}}=\frac{904.78in^3}{2}=452.39in^3[/tex]
Now, we need to find the volume of the cylinder:
[tex]V_{\text{cylinder}}=\pi\cdot r^2\cdot h=\pi\cdot(6)^2\cdot13=1470.27in^3[/tex]
Now, we need to sum both volumes:
Total volume = 452.39 in^3 + 1470.27 in^3 = 1922.66 in^3 (option C.)
