Volume of a Truncated Cone

Q: What is the formula for the volume of a truncated cone?

The formula is V = (π·h / 3)·(R² + R·r + r²), where R is the larger radius, r the smaller radius, h the height and π ≈ 3.1416.

Q: What is the surface area of a truncated cone?

It is calculated with A = π·s·(R + r) + π·(R² + r²), where s = √((R − r)² + h²) is the slant height.

Q: How many faces, edges and vertices does a truncated cone have?

It has 3 faces (two circles, the larger and smaller bases, plus the curved lateral surface), 2 curved edges and no vertices.

Q: What is the difference between a cone and a truncated cone?

A truncated cone is a cone whose tip has been cut off by a plane parallel to the base, so instead of ending in an apex it has a second, smaller circular base.

Volume =

π×height×(R²+R×r+r²)/3

Volume calculator for a truncated cone

Enter the larger radius (R), the smaller radius (r) and the height (h) of the truncated cone and you will be able to calculate the volume automatically

Larger radius (R)

Smaller radius (r)

Height (h)

Volume

Description, how many faces, edges and vertices are there in a truncated cone

A truncated cone is a cone with its tip cut off by a plane parallel to the base. It has two circular faces (a larger base and a smaller one) joined by a curved lateral surface, and it has no apex.

Examples of a truncated cone

You can find many truncated-cone-shaped objects: a bucket, a flowerpot, a plastic cup, a coffee filter or a lampshade. Can you think of any others? Leave us a comment in the box at the bottom of the page.

Formula for the volume of a truncated cone

To calculate the volume of a truncated cone you need the larger radius (R), the smaller radius (r) and the height (h). Multiply π by the height and by (R² + R×r + r²), then divide by 3. You can also use the online tool to calculate the volume automatically.

Volume =

π×height×(R²+R×r+r²)/3

Surface area of a truncated cone

The total area adds the lateral surface and the two circular bases, where s is the slant height: s = √((R − r)² + height²).

A = π×s×(R + r) + π×(R² + r²) [m²]

Worked example: volume of a truncated cone

Truncated cone with a larger radius of 6 cm, a smaller radius of 3 cm and a height of 8 cm:

V = (π × height × (R² + R×r + r²)) ÷ 3

V = (π × 8 × (36 + 18 + 9)) ÷ 3 = (π × 8 × 63) ÷ 3

V = 1,583.4 ÷ 3 ≈ 527.8 cm³

Frequently asked questions about the volume of a truncated cone

What is the formula for the volume of a truncated cone?

The formula is V = (π·h / 3)·(R² + R·r + r²), where R is the larger radius, r the smaller radius, h the height and π ≈ 3.1416.

How do you calculate the volume of a truncated cone step by step?

Add R² + R×r + r², multiply it by π and by the height, and divide by 3. For example, with R = 6 cm, r = 3 cm and a height of 8 cm the volume is ≈ 527.8 cm³.

What is the surface area of a truncated cone?

It is calculated with A = π·s·(R + r) + π·(R² + r²), where s = √((R − r)² + h²) is the slant height.

How many faces, edges and vertices does a truncated cone have?

It has 3 faces (two circles, the larger and smaller bases, plus the curved lateral surface), 2 curved edges and no vertices.

What is the difference between a cone and a truncated cone?

A truncated cone is a cone whose tip has been cut off by a plane parallel to the base, so instead of ending in an apex it has a second, smaller circular base.