Conical Frustum Calculator

Conical Frustum Calculator

Enter the radius of the top base of the frustum in units (e.g., 3)
Enter the radius of the bottom base of the frustum in units (e.g., 5)
Enter the height of the frustum in units (e.g., 4)

A conical frustum calculator is designed to compute various measurements related to a truncated cone, also known as a conical frustum.

The conical frustum calculator determines properties such as volume, surface area, and height based on input parameters like radii and slant height.

You’re designing a lampshade with a conical frustum shape. You know the radius of the top opening is 10 cm, the bottom radius is 20 cm, and the slant height is 30 cm. Using a this calculator, you can quickly determine the volume of material needed and the surface area to be covered, saving time on manual calculations and reducing the chance of errors.

Conical Frustum Calculation Chart

ParameterSymbolValueUnit
Top Radiusr10cm
Bottom RadiusR20cm
Slant Heights30cm
Heighth28.72cm
Lateral Surface AreaL2827.43cm²
Total Surface AreaA4084.07cm²
VolumeV12060.30cm³

Conical Frustum Formula

The primary formulas for a conical frustum are:

Volume: V = (1/3) pi h (R^2 + r^2 + Rr)

Lateral Surface Area: L = pi (R + r) s

Total Surface Area: A = pi (R^2 + r^2 + (R + r)s)

Height: h = sqrt(s^2 – (R – r)^2)

Let’s use our lampshade example to illustrate these formulas:

Volume:
V = (1/3) pi 28.72 (20^2 + 10^2 + 20 10) ≈ 12060.30 cm³

How to Calculate Volume of Frustum?

To calculate the volume of a frustum, we use the formula:

V = (1/3) pi h (R^2 + r^2 + Rr)

Calculate the height (h) using the Pythagorean theorem: h = sqrt(30^2 – (20 – 10)^2) ≈ 28.72 cm

Plug the values into the volume formula:

V = (1/3) pi 28.72 (20^2 + 10^2 + 20 10)
V ≈ 12060.30 cm³

This result tells us that our lampshade will enclose about 12 liters of space.

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