Answer: [tex]2,034.72\ mm^3[/tex]
Step-by-step explanation:
The missing part is: "A cylinder and 2 half spheres. All have a radius of 6 millimeters. The cylinder has a height of 10 millimeters."
You need to use the following formulas to solve the exercise:
1. The volume of a cylinder can be calculated with:
[tex]V_{c}=\pi r^2h[/tex]
Where "r" is the radius and "h" is the height.
2. The volume of a sphere can be calculated with:
[tex]V_{s}=\frac{4}{3}\pi r^3[/tex] Where "r" is the radius.
In this case you know that the cylinder and the sphere have a radius of 6 millimeters and the height of cylinder is 10 millimeters. Then, you can substitute values into each formula in order to find the volumes:
[tex]Vc=(3.14)(6\ mm)^2(10\ mm)\\\\Vc=1,130.4\ mm^3\\\\\\Vs=\frac{4}{3}(3.14)(6\ mm)^3\\\\Vs=904.32\ mm^3[/tex]
Adding them, you get that the volume of the composite figure is:
[tex]V_{CF}=1,130.4\ mm^3+904.32\ mm^3\\\\V_{CF}=2,034.72\ mm^3[/tex]
