Finding the volume of a cone has never been easier thanks to this online cone volume calculator. To calculate the volume of a cone, simply enter the height and radius of the conical shape.
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Cones are three-dimensional objects with a circle at one end and a point at the other. A triangular solid is formed by the depth of a cone.
In the above standard cone figure, ‘r’ represents the radius of the cone and ‘h’ represents the height of the cone.
Volume of Cone Calculator Use
- To calculate the volume of conical shaped items, use this cone volume calculator.
- In the above calculator, enter the cone’s height and radius in the appropriate fields.
- The calculator will display the volume of a cone based on the information entered.
Cone Volume Formula
A simple formula can be used to calculate the volume of a cone. Using the formula below, we can calculate the volume of a cone using the radius (r) and height (h) of the cone.
How to Calculate the Volume of a Cone
In geometry class, everyone learned how to calculate the volume of a cone. However, not everyone recalls this after they have graduated from high school. If you know the radius and height of the conical-shaped object, calculating the volume is simple. You can easily calculate the volume of the cone using the above formula. We’ve solved some step-by-step examples below to assist you in calculating the cone volume.
Example
1. The birthday hat has a radius of 10 inches and a height of 18 inches. Calculate the volume of the birthday hat, which is conical in shape.
Solution :
Radius of hat (r) = 10 in
Height of the birthday hat (h) = 18 in
Using the cone volume formula,
Volume = (1/3) x π r² h
Volume = (1/3) x 3.141592654 x 102 x 18
Volume = 1884.95559 cu.in
The volume of the birthday hat is 1884.95559 cubic inches.
Example
2. An ice cream cone’s height is 12 inches, while its base diameter is 4 inches. Determine how much ice cream it can hold.
Solution :
Height of ice cream cone = 12 inch
Diameter of cone = 4 inch
The radius of the cone is required to utilise the cone volume formula, but the diameter of the ice cream cone is given instead. First, we must determine the radius of the cone.
The radius of a circle is always half its diameter. As a result, the radius of the cone is,
Radius = (1/2)x diameter
Radius = (1/2)x 4
Radius = 2 inch
Using the cone volume formula,
Volume = (1/3) x π r² h
Volume = (1/3) x 3.141592654 x 22 x 12
Volume = 50.2655 cu.in
The ice cream cone can hold 50.2655 cubic inches volume of ice cream.
How to Calculate the Volume of a Truncated Cone
Truncated cones are similar to basic cones in appearance. The only difference is that it lacks a pointed side and instead has a circular side that is smaller than the bottom circle. In simple terms, a truncated cone can be created by cutting the pointed top side of the cone. The illustration below can help you understand what a truncated cone is.
The truncated cone’s dimensions are quite similar to those of a normal cone. The only difference is that a normal cone has one radius, whereas a truncated cone has two, one smaller and one larger. We’ve included some examples of how to calculate the volume of a truncated cone down below.
Example
A truncated cone’s base and top radius are 6 mm and 3 mm, respectively. Find the volume of the truncated cone if the height is 70 mm.
Solution :
height of cone = 70 mm
base radius (R) = 6 mm
top radius (r) = 3 mm
Now that we have all of the information needed to determine the volume of a truncated cone, we must use a formula that is slightly different from the standard cone volume formula. Because a truncated cone has two radiuses, apply the formula below to calculate its volume.
Using the formula,
Volume = (1/3) x πh(R2 + Rr + r2)
Volume = (1/3) x (3.141592654 x 70) x ( 62 + {6 x 3} + 32 )
Volume = 4618.1412 mm3
The volume of truncated cone is 4618.1412 mm3