Volume of Cone Calculator

A cone is a three-dimensional shape that has a circular base and a single vertex. To calculate the volume of a cone we will need to multiply the area of the base (i.e, the area of the circle = π * r²) by the height of the cone, and by ⅓.

Volume = (1/3) * π * r² * h

Then, Steps to calculate the volume of cone

Step 1: Find the height of the cone and enter it.

Step 2: Find the radius of the circular base and enter it

Step 3: Click on the volume option, and the volume of the cone will appear.

Note: Remember, make sure that all the measurements are in the same unit before calculating the volume. You can also easily convert the measurements into required units by using the unit converter tools on our website.

A truncated cone is a three-dimensional figure in which the top part is cut off. And the cut is perpendicular to the height of the cone. We can calculate the volume of the cone by subtracting the cut off part from the whole part of the cone. Or we can use the following formula:

Volume = (1/3) * π * depth * (r² + r * R + R2)

Where, R = radius of the base of the cone, and r = radius of the top surface of the cone.

An oblique cone is a three-dimensional figure or shape that has an apex which is not aligned above the center of the base. It seems leaning towards one side, like that of an oblique cylinder.

Note: The formula of the volume of an oblique is the same as the formula of the volume of a right one

Here are some of the examples to help you understand the formula of volume of the cone.

Example 1: Find out the volume of a cone of the height if the cone is 4 in and the base radius is 3 in.

Solution: Given: Radius r = 3 in

Height h = 4 in

Volume of Cone = (⅓ π r2 h)

= ⅓ * π * (32) * 4

= ⅓ × 3.14 × 32 × 4

= 37.68 in3

Example 2: Find the volume of a cone, if the radius of the cone is 4 cm and the height is 9 cm.

Solution:Given: Radius r = 4 cm

Height h = 9 cm

Volume of Cone = (⅓ π r2 h)

= ⅓ * π * (42) * 9

= ⅓ × 3.14 × 16 × 9

= 150.72 cm3

Example 3:A right triangle ABC with sides 6 cm, 14 cm and 17 cm is revolved about the side 14 cm. Find the volume of the solid so obtained.

Solution: As the triangle revolved about the side 12 cm.

Therefore, Radius r = 5 cm and

Height h = 12 cm

Volume of Cone = (⅓ π r2 h)

= ⅓ * π * (52) * 12

= ⅓ × 3.14 × 25 × 12

= 314 cm3

Question: What dimensions do we need to find the volume of the cone?

Answer: In order to find the volume of cone dimensions and measurements, we can simply apply the formula for the area of a circle for one of the bases of the cone and then multiply it by one-third of the height of the cone. This formula is very identical with the formula of volume of cylinder and prism.

Question: If the volume of the cone and the height of the cone is already given then, how do I find out the radius of the cone?

Answer: If the volume and height of the cone are already given, simply put the given values according to the formula of the volume of the cone.

Write, volume = ⅓ * π * r2 * h

Put the given values and solve the equation on the left side until the given volume, multiplication of ⅓ × π × h and r2 is left.

Now, put the r2 on the right side and divide the volume by the multiplied value of ⅓ × π × h. Find the square root of the answer.

That is your radius.

Question: How to find the radius and the volume of the cone if the diameter of the circular base is given?

Answer:To find out the radius of the cone, simply divide the given diameter of the cone by 2, as the radius is half of the value of the diameter of a circle.

Then, to find the volume of the radius, put all the given values in the formula of the volume of cone i.e., (⅓ π r2 h).

Question: Which measurement unit is used to represent the volume of a cone?

Answer:The volume of the cone is always measured in cubic units. For example - cm3, in3, m3, mm3 etc.