Answer:
106.21π cubic centimeters
Step-by-step explanation:
The volume of this figure can be determined by treating it as a cone and a hemisphere.
Cone
The volume of a cone can be determined with the formula [tex]V = \pi r^{2} \frac{h}{3}[/tex], where r is the radius of the base, and h is the height.
The diameter is given as 8.3 and, as the radius is half of the diameter, we can determine that the radius is 4.15.
With the radius as 4.15 and the height as 10.2, we can substitute and solve:
[tex]V = \pi (4.15)^{2} \frac{(10.2)}{3}\\V = \pi (17.2225) (3.4)\\V = 58.5565 \pi[/tex]
Hemisphere
The volume of a hemisphere can be determined with the formula [tex]V = \frac{2}{3} \pi r^{3}\\[/tex], where r is the radius. With this we can solve:
[tex]V = \frac{2}{3} \pi (4.15)^{3}\\V = \frac{2}{3} \pi (71.473375)\\V = 47.64891...\pi\\\\[/tex]
Total Volume
Adding the two volumes together, we get a total volume of 106.21π cubic centimeters
