Cone Calculator (Volume & Surface Area)
Cone Calculator (Volume & Surface Area)
A cone tapers smoothly from a circular base to a single point (the apex) - ice cream cones, traffic cones, and funnels are everyday examples. Enter the radius and height (in whatever unit you like), and this calculator finds the slant height (the distance along the cone's surface from the base edge to the apex), the volume, and both the lateral and total surface area, along with a diagram and the full step-by-step working.
- V = ⅓πr²h, exactly one-third the volume of a cylinder with the same base and height - a cone with radius 3 and height 4 has a volume of ⅓ × π × 3² × 4 ≈ 37.70 cubic units.
- The slant height is l = √(r² + h²), found with the Pythagorean theorem - for radius 3 and height 4, that's the classic 3-4-5 triangle, giving a slant height of exactly 5.
- Total SA = πr(r + l) combines the circular base (πr²) with the lateral surface (πrl, the "unrolled" cone side) - for radius 3, height 4 (slant 5), that's π × 3 × (3 + 5) ≈ 75.40 square units.
How do I find the volume of a cone?
Use V = ⅓πr²h. A cone with radius 3 and height 4 has a volume of ⅓ × π × 3² × 4 ≈ 37.70.
What is the slant height of a cone?
It's the distance from the edge of the base to the apex, measured along the cone's surface: l = √(r² + h²). For radius 3 and height 4, l = √(9+16) = √25 = 5.
Cone Calculator (Volume & Surface Area)
A cone tapers smoothly from a circular base to a single point (the apex) - ice cream cones, traffic cones, and funnels are everyday examples. Enter the radius and height (in whatever unit you like), and this calculator finds the slant height (the distance along the cone's surface from the base edge to the apex), the volume, and both the lateral and total surface area, along with a diagram and the full step-by-step working.
- V = ⅓πr²h, exactly one-third the volume of a cylinder with the same base and height - a cone with radius 3 and height 4 has a volume of ⅓ × π × 3² × 4 ≈ 37.70 cubic units.
- The slant height is l = √(r² + h²), found with the Pythagorean theorem - for radius 3 and height 4, that's the classic 3-4-5 triangle, giving a slant height of exactly 5.
- Total SA = πr(r + l) combines the circular base (πr²) with the lateral surface (πrl, the "unrolled" cone side) - for radius 3, height 4 (slant 5), that's π × 3 × (3 + 5) ≈ 75.40 square units.
How do I find the volume of a cone?
Use V = ⅓πr²h. A cone with radius 3 and height 4 has a volume of ⅓ × π × 3² × 4 ≈ 37.70.
What is the slant height of a cone?
It's the distance from the edge of the base to the apex, measured along the cone's surface: l = √(r² + h²). For radius 3 and height 4, l = √(9+16) = √25 = 5.