Conical Frustum Calculator
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
Parameter | Symbol | Value | Unit |
---|---|---|---|
Top Radius | r | 10 | cm |
Bottom Radius | R | 20 | cm |
Slant Height | s | 30 | cm |
Height | h | 28.72 | cm |
Lateral Surface Area | L | 2827.43 | cm² |
Total Surface Area | A | 4084.07 | cm² |
Volume | V | 12060.30 | cm³ |
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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