Volume of Frustum Cone Calculator

Use the volume of frustum cone calculator and find the volume and different properties of a conical frustum by giving 2 radii and 1 other known value.

What Is The Volume of Frustum of Cone?

When a cone is cut from the top then the shape that is formed is known as the frustum. It is also known as the truncated cone. The volume of frustum represents the space that is available inside the frustum.

Volume of Frustum of Cone Formula:

The frustum volume formula is as follows:

Volume = 1/3πh(r1^2+ r1xR2 + r2^2)

Where

• r1 represents the radius of the top
• R2 is the radius of the bottom
• h is the height
• s show the slant height
• V is the volume
• π = pi = 3.1415926535898

Conical Frustum Formulas In Terms of r And h:

Let’s take a look at the following Conical Formulas:

The slant height of a conical frustum:

s = √((r1 – r2)^2 + h^2)

Volume of a conical frustum:

V = (1/3) * π * h * (r1^2 + r2^2 + (r1 * r2))

The lateral surface area of a conical frustum:

S = π * (r1 + r2) * s = π * (r1 + r2) * √((r1 – r2)^2 + h^2)

Top surface area of a conical frustum: 

T = πr1^2

The base surface area of a conical frustum: 

B = πr2^2

The total surface area of a conical frustum:

A = π * (r1^2 + r2^2 + (r1 + r2) * s) = π * [ r1^2 + r2^2 + (r1 + r2) * √((r1 – r2)^2 + h^2) ]

The most reliable and easy way to find the volume of frustum of a cone is by using the volume of frustum cone calculator. It just requires inputting the known values and provides you with precise volume without much effort. 

How To Calculate The Volume of Conical Frustum?

Use the below-mentioned formulas to find the volume and other related unknown terms of the conical frustum:

If radius1, radius2, and height are given then calculate the slant height, volume of frustum of a cone, lateral surface area, and total surface area, then use the above formulas.
Given r1, r2, h find s, V, S, A

If the radius1, radius2, and slant height are given then calculate the height, volume, lateral surface area, and total surface area, using the following height formula and the above-mentioned formulas:
Given r1, r2, s find h, V, S, A

• h = √(s^2 – (r1 – r2)^2)

When the radius1, radius2, and volume of frustum cone are given, then calculate the height, slant height, lateral surface area, and total surface area by finding the height as:

Given r1, r2, V find h, s, S, A

• h = (3 * V) / (π * (r1^2 + r2^2 + (r1 * r2)))

If radius1, radius2, and lateral surface area are available then find the height, slant height, volume, and total surface area then find s and h with the help of the following forms:
Given r1, r2, S find h, s, V, A

• s = S / (π * (r1 + r2))
• h = √(s^2 – (r1 – r2)^2)

When radius1, radius2, and total surface area are available then calculate the height, slant height, lateral surface area, and volume of frustum of a cone, Find the s and h by using the following formulas:
Given r1, r2, A find h, s, V, S

• s = [A/π – r1^2 – r2^2] / (r1 + r2)
• h = √(s^2 – (r1 – r2)^2)

Example:

Suppose you have a frustum which is obtained by removing a smaller cone with a base radius of 8 cm from the bigger cone that has a base radius of 20 cm. The height of the frustum is 10 cm find the volume.

Solution:

Given that:

R1 (radius of the larger base) = 20 cm

R2 (radius of the smaller base) = 8 cm

h (height) = 10 cm

Now, put these values into the frustum of cone volume formula:

Volume = (1/3) x π x 10 cm x (20^2 + 8^2 + (20 x 8))

Volume = (1/3) x π x 10 cm x (400 + 64 + 160)

Volume = (1/3) x π x 10 cm x 624

Volume = 6,186.67 cm³

If you want to save time and effort, then simply get the assistance of a truncated cone volume calculator. It will allow you to quickly find the volume of a frustum of a cone by just giving a few inputs.