Answer:
726.65 cubic inches
Step-by-step explanation:
We are going to assume that the head, middle and bottom are spheres.
The formula to get the volume of a sphere is
[tex]V= \frac{4}{3}\pi r^{2}[/tex] where r is the radius of the sphere.
Now, let's proceed to apply this formula to the 3 spheres of the snowman:
The head is 12 inches wide (diameter), thus, the radius would be 6 inches:
[tex]V= \frac{4}{3}\pi r^{2}\\V= \frac{4}{3}\pi 6^{2}\\V= \frac{4}{3}\pi 36\\V=\frac{144\pi }{3} \\V=38\pi[/tex] cubic inches
The middle is 16 inches wide (diameter), thus, the radius would be 8 inches.
[tex]V= \frac{4}{3}\pi r^{2}\\V= \frac{4}{3}\pi 8^{2}\\V= \frac{4}{3}\pi 64\\V=\frac{256\pi }{3} \\V=85.3\pi[/tex] cubic inches
The bottom is 18 inches wide (diameter), thus the radius would be 9 inches.
[tex]V= \frac{4}{3}\pi r^{2}\\V= \frac{4}{3}\pi 9^{2}\\V= \frac{4}{3}\pi 81\\V=\frac{324\pi }{3} \\V=108\pi[/tex] cubic inches.
Now, to get the total volume of the snowman we're going to sum up the volume of all three spheres:
Total volume = [tex]38\pi +85.3\pi +108\pi =231.3\pi[/tex] cubic inches.
If we take pi = 3.1416,
Total volume = [tex]231.3(3.1416)=726.65[/tex] cubic inches.
