How to Find the Radius of a Cylinder
A cylinder is a three-dimensional shape with two parallel circular bases connected by a curved surface. The radius of a cylinder refers to the radius of its circular base and is essential for calculating volume, surface area, and other properties.
Cylinder Radius Formulas
From Volume + Height
Given V = pi * r^2 * h, solve for r.
r = sqrt(V / (pi * h))
From Surface Area + Height
Given SA = 2*pi*r^2 + 2*pi*r*h, solve using the quadratic formula.
r = (-h + sqrt(h^2 + SA/pi)) / 2
Cylinder Properties
- Volume: V = pi * r^2 * h -- the space enclosed by the cylinder
- Lateral Surface Area: LSA = 2 * pi * r * h -- the curved surface
- Total Surface Area: TSA = 2 * pi * r * (r + h) -- curved surface plus two circular bases
- Diameter: d = 2r -- the width across the circular base
Surface Area Method Explained
Finding the radius from the total surface area requires solving a quadratic equation. The formula SA = 2*pi*r^2 + 2*pi*r*h can be rearranged to 2*pi*r^2 + 2*pi*h*r - SA = 0, which is a standard quadratic in r. We take the positive root using the quadratic formula.
Real-World Applications
- Engineering: designing pipes, tanks, and cylindrical vessels
- Manufacturing: sizing cans, bottles, and cylindrical containers
- Construction: columns, pillars, and cylindrical structures
- Science: measuring test tubes, beakers, and cylindrical samples