The volume of the styrofoam collar is approximately 1,960.35 [tex]in^{3} .[/tex]
Step-by-step explanation:
Step 1:
The given styrofoam collar is a hollow cylinder. A hollow cylinder consists of an outer radius and an inner radius.
This given hollow cylinder has an outer radius of 8 inches and an inner radius of 5 inches. The height of the cylinder is 16 inches.
To calculate the volume of a hollow cylinder we subtract the volume of a cylinder constructed with the inner radius from the volume of a cylinder with the outer radius.
Step 2:
The volume of a cylinder, [tex]V = \pi r^{2} h.[/tex]
For the outer cylinder, [tex]r = 8[/tex] inches and [tex]h=16[/tex] inches.
The volume of the outer cylinder, [tex]V_{1} = \pi (8^{2})(16) = 3,216.99.[/tex]
For the inner cylinder, [tex]r = 5[/tex] inches and [tex]h=16[/tex] inches.
The volume of the inner cylinder, [tex]V_{2} = \pi (5^{2})(16) = 1,256.637.[/tex]
Step 3:
The volume of the styrofoam collar [tex]= V_{1} -V_{2},[/tex]
The volume of the styrofoam collar [tex]= 3,216.99-1,256.637 = 1,960.353.[/tex]
Rounding this off, we get the volume of the styrofoam collar as 1,960.35 [tex]in^{3} .[/tex]
