An open topped cylinder has a volume of 125 cubic inches. Express the surface area of the cylinder as a function of its radius.
radius --- r
height --- h
V= πr^2 h
125/(πr^2) = h
SA , assume there is a bottom
SA = πr^2 +2πr h
= πr^2 = 2πr(125/(πr^2)
= πr^2 + 250/r
To express the surface area of an open-topped cylinder as a function of its radius, we need to consider two main components: the lateral surface area and the base area.
The lateral surface area of a cylinder can be found using the formula A = 2πrh, where A is the lateral surface area, π is the mathematical constant pi (approximately 3.14159), r is the radius, and h is the height. However, in this case, the height of the cylinder is not given, only the volume.
The volume of a cylinder can be found using the formula V = πr^2h, where V is the volume, π is pi, r is the radius, and h is the height. We are given that the volume is 125 cubic inches.
Since the cylinder is open-topped, we can assume that the height of the cylinder extends indefinitely. Therefore, we can rewrite the formula for the volume as h = V / (πr^2).
Substituting this value of h into the formula for the lateral surface area, we get A = 2πrh = 2πr(V / (πr^2)). Simplifying this equation further gives A = 2V / r.
Thus, the surface area of the cylinder as a function of its radius is A(r) = 2V / r, where V is the given volume of 125 cubic inches.