Cone Calculator

Cone is evaluated from Base Radius and Height. The calculation reports Volume, Lateral Surface Area and Total Surface Area.

Results

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About the Cone Calculator

Cone is treated here as a quantitative relation between Base Radius and Height and Volume, Lateral Surface Area, Total Surface Area and Slant Height.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
Slant height l is the straight-line distance from tip to base edge. Lateral area = pirl (unfolds into a sector of a circle). Volume = (1/3) base area x height, same as any pyramid.

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

Slant height l is the straight-line distance from tip to base edge. Lateral area = pirl (unfolds into a sector of a circle). Volume = (1/3) base area x height, same as any pyramid.

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Ice cream cone (r = 2.5 cm, h = 10 cm)

Inputs

radius: 2.5 height: 10
Volume: 65.4498 cubic units. Lateral Surface Area: 80.957 sq units. Total Surface Area: 100.5919 sq units. Slant Height: 10.3078 units. Base Area: 19.635 sq units

With Base Radius = 2.5 and Height = 10 as the stated inputs, the result is Volume = 65.4498 cubic units, Lateral Surface Area = 80.957 sq units and Total Surface Area = 100.5919 sq units. Each value corresponds to the declared output fields.

Example 2: Traffic cone (r = 6 in, h = 18 in)

Inputs

radius: 6 height: 18
Volume: 678.584 cubic units. Lateral Surface Area: 357.6452 sq units. Total Surface Area: 470.7425 sq units. Slant Height: 18.9737 units. Base Area: 113.0973 sq units

With Base Radius = 6 and Height = 18 as the stated inputs, the result is Volume = 678.584 cubic units, Lateral Surface Area = 357.6452 sq units and Total Surface Area = 470.7425 sq units. Each value corresponds to the declared output fields.

Example 3: Funnel/conical tank (r = 1 ft, h = 3 ft)

Inputs

radius: 1 height: 3
Volume: 3.1416 cubic units. Lateral Surface Area: 9.9346 sq units. Total Surface Area: 13.0762 sq units. Slant Height: 3.1623 units. Base Area: 3.1416 sq units

With Base Radius = 1 and Height = 3 as the stated inputs, the result is Volume = 3.1416 cubic units, Lateral Surface Area = 9.9346 sq units and Total Surface Area = 13.0762 sq units. Each value corresponds to the declared output fields.

Example 4: Volcano simulation (r = 50 m, h = 100 m)

Inputs

radius: 50 height: 100
Volume: 261,799.3878 cubic units. Lateral Surface Area: 17,562.0368 sq units. Total Surface Area: 25,416.0185 sq units. Slant Height: 111.8034 units. Base Area: 7,853.9816 sq units

With Base Radius = 50 and Height = 100 as the stated inputs, the result is Volume = 261,799.3878 cubic units, Lateral Surface Area = 17,562.0368 sq units and Total Surface Area = 25,416.0185 sq units. Each value corresponds to the declared output fields.

Common Use Cases

  • Calculate cone volume from radius and height
  • Find lateral surface area of a cone
  • Compute slant height for construction projects