Answer:
16.75 cubic inches
Step-by-step explanation:
Key skills needed: Volume of a cylinder, Volume of a sphere
1) To get the answer to this problem, you need to understand two formulas: The volume of a sphere, and The volume of a cylinder.
- Volume of a sphere --> [tex]V= \frac{4}{3}\pi r^3[/tex] (V = volume, and r = radius)
- Volume of a cylinder --> [tex]V = \pi r^2h[/tex] (V = volume, r = radius,h = height)
These formulas will be needed.
2) In order to solve this problem, we need to find the volumes of both, and the subtract them from one another to find the difference.
3) Let's start by finding the volumes:
- Cylinder --> [tex]V = \pi r^2h[/tex]
We have the radius (which is 2) and the height (which is 4)
- This means we can solve --> [tex]V = \pi(2^2)(4)[/tex]
- 2 squared is 4, so then it would be --> [tex]V = \pi (4)(4)[/tex]
- 4 times 4 is 16 so [tex]V = 16\pi[/tex] ---> 16 pi is the same as 50.24 cubic inches (if you use 3.14 as pi).
- Next is the Sphere--> [tex]V = \frac{4}{3}\pi r^3[/tex]
We have the radius (which is 2) so we can solve
- [tex]V = \frac{4}{3}\pi (2^3)[/tex]
- 2 cubed is 8, so it would be --> [tex]V = \frac{4}{3}\pi (8)[/tex]
- 8 times 4/3 is 32/3 so --> [tex]V = \frac{32}{3}\pi[/tex] --> which is Around 33.51 cubic inches
4) Now we have to find the difference, so we do:
This means your answer would be 16.75 as that is the closest one.
Hope you understood and have a nice day!! :D
