How to Calculate the Surface Area and Volume of a Cone
A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the center of base) called the apex or vertex
Important Parameters of a Cone
- Radius (r) – The distance from the center to the edge of the base.
- Height (h) – The perpendicular distance from the apex to the center of the base.
- Slant Length (l) – The distance from the apex to any point on the circular edge of the base.
For Example
- Radius (r) = 1 m
- Height (h) = 4 m
- Slant Length (l) = 4.123 m
1. Formula For curved Surface Area = πrl
2. Formula For Total Surface Area = πrl + πr²
3. Formula Volume =π²h
Step 1: Surface Area of a Cone
Formula for Surface Area of cone = Curved Surface area + Base area
1. Curved Surface Area= πrl
Where,
- π – 3.14
- r – Radius
- l – Length
Calculation: = (3.14 x 1 x 6) = 12.956 m²
2. Base area= πr²
Calculation: = (3.14 x 1 x 4.123) + (3.14 x 1²) = 16.097 m²
Result:
The Curved surface area of the cone is 12.956 m².
The Total surface area of the cone is 16.097 m²
Step 2: Volume of a Cone
Formula for Volume of cone:
Volume of cone =π²h)
Where:
- π – 3.14
- r – Radius
- h – Height
Calculation: = (1/3) (3.14 x 1² x 4) = 4.19m³
Result:
The total Volume of the cone is 4.19m³