How to Find the Radius of a Cone
A cone is a three-dimensional geometric shape with a circular base that tapers to a point called the apex. The radius of the base circle is one of the key dimensions needed to compute volume, surface area, and slant height.
Cone Radius Formulas
From Volume + Height
Given V = (1/3) pi r^2 h, solve for r.
r = sqrt(3V / (pi * h))
From Slant Height + Height
Use the Pythagorean theorem: l^2 = r^2 + h^2.
r = sqrt(l^2 - h^2)
From Lateral Surface Area
Given LSA = pi * r * l, solve for r.
r = LSA / (pi * l)
Cone Properties
- Volume: V = (1/3) * pi * r^2 * h
- Lateral Surface Area: LSA = pi * r * l
- Total Surface Area: TSA = pi * r * (r + l)
- Slant Height: l = sqrt(r^2 + h^2)
Real-World Applications
- Architecture: designing conical roofs and towers
- Manufacturing: creating funnels, ice cream cones, traffic cones
- Engineering: calculating material for conical vessels and tanks
- Science: understanding volcanic cones and particle physics