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Volume of Frustum Cone Calculator

Find the volume of the frustum cone and other unknown measurements (surface area, slant heights, etc.) with this online tool

Choose a Calculation:

Height (r₁)

cm ▾

Height (r₂)

cm ▾

Radius (h)

cm ▾

Units π

Let pi:

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Volume of Frustum Cone Calculator

Use the volume of frustum cone calculator to find the volume and other properties of a conical frustum by providing two radii and one additional known value.

What Is the Volume of a Frustum of a Cone?

A frustum is formed when the top of a cone is cut off. It is also called a truncated cone. The volume of a frustum represents the space contained inside it.

Volume Formula for a Conical Frustum

The volume is given by:

V = (1/3) × π × h × (r1² + r1 × r2 + r2²)

r1 = radius of the top
r2 = radius of the bottom
h = height of the frustum
s = slant height
V = volume
π ≈ 3.1415926535898

Other Important Formulas

Slant height:

s = √((r1 - r2)² + h²)

Lateral surface area:

S = π × (r1 + r2) × s = π × (r1 + r2) × √((r1 - r2)² + h²)

Top surface area:

T = π × r1²

Bottom surface area:

B = π × r2²

Total surface area:

A = π × [r1² + r2² + (r1 + r2) × s] = π × [r1² + r2² + (r1 + r2) × √((r1 - r2)² + h²)]

How to Calculate the Volume of a Conical Frustum

Depending on the known values, use the following formulas:

Given r1, r2, h → find s, V, S, A
Given r1, r2, s → h = √(s² - (r1 - r2)²), then find V, S, A
Given r1, r2, V → h = (3 × V) / (π × (r1² + r2² + r1 × r2)), then find s, S, A
Given r1, r2, lateral surface area S → s = S / (π × (r1 + r2)), h = √(s² - (r1 - r2)²), then find V, A
Given r1, r2, total surface area A → s = [A / π - r1² - r2²] / (r1 + r2), h = √(s² - (r1 - r2)²), then find V, S

Example

Find the volume of a frustum obtained by cutting a smaller cone (radius 8 cm) from a larger cone (radius 20 cm) with a height of 10 cm.

Solution:

r1 (top radius) = 8 cm
r2 (bottom radius) = 20 cm
h (height) = 10 cm

Volume formula:

V = (1/3) × π × h × (r1² + r1 × r2 + r2²)

Substitute the values:

V = (1/3) × π × 10 × (8² + 8 × 20 + 20²)

V = (1/3) × π × 10 × (64 + 160 + 400)

V = (1/3) × π × 10 × 624

V ≈ 6,186.67 cm³

To save time and effort, you can use a truncated cone volume calculator to quickly determine the volume and other properties by entering a few known values.

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