Question 459588: Find a polynomial that represents the total surface area of the right circular cylinder with a radius of 4.
Now use that polynomial to determine the total surface area of each of the following right circular cylinders that have a base with a radius of 4. Use 3.14 for π, and express the answers to the nearest tenth.
Answer by math-vortex(648)   (Show Source):
You can put this solution on YOUR website! A right circular cylinder is a cylinder whose base is perpendicular to its sides (like a soup can.) The expression for the surface area has two parts:
There is the rectangular-shaped side that wraps around the cylinder, and the circular base and top of the cylinder.
.
The surface area of the side is the height of the cylinder times the circumference of the base. In algebra, this translates to
.
(h)(2[pi]r)
.
where h is the height of the cylinder and r is the radius of its circular base. We know that the radius is 4 and we approximate [pi] as 3.14. This gives us
.
h(2)(3.14)(4) = (25.12)h
The surface area of the base and top of the cylinder is the area of the circle. There are two circles so we multiply by 2.
.
(2)([pi])r^2 = (2)(3.14)(4^2) = 100.48
.
We combine these expressions to create a polynomial for the surface area S in terms of the height of the cylinder.
====
S = (25.12)h + 100.48
====
Your question does not include information about the other cylinders, but you can substitute their heights for h in the polynomial and get the surface area.
.
Good luck!
|
|
|
