Cone Calculator
Calculate volume, surface area, and slant height of a cone.
Slant Height (l) = sqrt(r^2 + h^2)\nVolume = (1/3) * PI * r^2 * h\nBase Area = PI * r^2\nLateral Surface Area = PI * r * l\nTotal Surface Area = Base Area + Lateral Area
Example:\nRadius (r) = 5 cm\nHeight (h) = 12 cm\n\nSlant Height = sqrt(5^2 + 12^2) = sqrt169 = 13 cm\nVolume = (1/3) * PI * 5^2 * 12 = 314.16 cm^3\nBase Area = PI * 5^2 = 78.54 cm^2\nLateral Area = PI * 5 * 13 = 204.20 cm^2\nTotal Area = 78.54 + 204.20 = 282.74 cm^2
What is a cone?
A 3D shape with a circular base and a point (apex) at the top. Think of an ice cream cone or traffic cone.
How do you find slant height?
Slant height (l) = sqrt(r^2 + h^2), using the Pythagorean theorem on the right triangle formed by radius, height, and slant.
What is lateral surface area?
The curved surface area (not including the base). Formula: PI * r * l, where l is slant height.
Why is volume divided by 3?
A cone is 1/3 the volume of a cylinder with the same base and height. V = (1/3)PIr^2h.
What are real-world applications?
Calculating storage capacity of silos, volume of funnels, material for cone-shaped roofs, or ice cream portions.
🔗 Related Calculators
📐 Formula
Slant Height (l) = sqrt(r^2 + h^2)\nVolume = (1/3) * PI * r^2 * h\nBase Area = PI * r^2\nLateral Surface Area = PI * r * l\nTotal Surface Area = Base Area + Lateral Area
📝 Example Calculation
Example:\nRadius (r) = 5 cm\nHeight (h) = 12 cm\n\nSlant Height = sqrt(5^2 + 12^2) = sqrt169 = 13 cm\nVolume = (1/3) * PI * 5^2 * 12 = 314.16 cm^3\nBase Area = PI * 5^2 = 78.54 cm^2\nLateral Area = PI * 5 * 13 = 204.20 cm^2\nTotal Area = 78.54 + 204.20 = 282.74 cm^2
❓ Frequently Asked Questions
What is a cone?▼
A 3D shape with a circular base and a point (apex) at the top. Think of an ice cream cone or traffic cone.
How do you find slant height?▼
Slant height (l) = sqrt(r^2 + h^2), using the Pythagorean theorem on the right triangle formed by radius, height, and slant.
What is lateral surface area?▼
The curved surface area (not including the base). Formula: PI * r * l, where l is slant height.
Why is volume divided by 3?▼
A cone is 1/3 the volume of a cylinder with the same base and height. V = (1/3)PIr^2h.
What are real-world applications?▼
Calculating storage capacity of silos, volume of funnels, material for cone-shaped roofs, or ice cream portions.