Volume of Frustum of Cone given Slant Height, Height and Top Radius Calculator

✖Height of Frustum of Cone is the maximum vertical distance from the bottom to the top circular face of the Frustum of the Cone.ⓘ Height of Frustum of Cone [h]			+10% -10%
✖Top Radius of Frustum of Cone is the distance between the center and any point on the circumference of the top circular surface of the Frustum of the Cone.ⓘ Top Radius of Frustum of Cone [r_Top]			+10% -10%
✖The Slant Height of Frustum of Cone is the length of the line segment joining the extremities of two parallel radii, drawn in the same direction of the two circular bases.ⓘ Slant Height of Frustum of Cone [h_Slant]			+10% -10%

✖Volume of Frustum of Cone is the quantity of three-dimensional space enclosed by the entire surface of the Frustum of the Cone.ⓘ Volume of Frustum of Cone given Slant Height, Height and Top Radius [V]

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Volume of Frustum of Cone given Slant Height, Height and Top Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Frustum of Cone = 1/3*pi*Height of Frustum of Cone*(Top Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))^2+(Top Radius of Frustum of Cone*(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))))
V = 1/3*pi*h*(r_Top^2+(r_Top-sqrt(h_Slant^2-h^2))^2+(r_Top*(r_Top-sqrt(h_Slant^2-h^2))))
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Volume of Frustum of Cone - (Measured in Cubic Meter) - Volume of Frustum of Cone is the quantity of three-dimensional space enclosed by the entire surface of the Frustum of the Cone.
Height of Frustum of Cone - (Measured in Meter) - Height of Frustum of Cone is the maximum vertical distance from the bottom to the top circular face of the Frustum of the Cone.
Top Radius of Frustum of Cone - (Measured in Meter) - Top Radius of Frustum of Cone is the distance between the center and any point on the circumference of the top circular surface of the Frustum of the Cone.
Slant Height of Frustum of Cone - (Measured in Meter) - The Slant Height of Frustum of Cone is the length of the line segment joining the extremities of two parallel radii, drawn in the same direction of the two circular bases.

STEP 1: Convert Input(s) to Base Unit

Height of Frustum of Cone: 8 Meter --> 8 Meter No Conversion Required
Top Radius of Frustum of Cone: 10 Meter --> 10 Meter No Conversion Required
Slant Height of Frustum of Cone: 9 Meter --> 9 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = 1/3*pi*h*(r_Top^2+(r_Top-sqrt(h_Slant^2-h^2))^2+(r_Top*(r_Top-sqrt(h_Slant^2-h^2)))) --> 1/3*pi*8*(10^2+(10-sqrt(9^2-8^2))^2+(10*(10-sqrt(9^2-8^2))))

Evaluating ... ...

V = 1619.44352236136

STEP 3: Convert Result to Output's Unit

1619.44352236136 Cubic Meter --> No Conversion Required

FINAL ANSWER

1619.44352236136 ≈ 1619.444 Cubic Meter <-- Volume of Frustum of Cone

(Calculation completed in 00.004 seconds)

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Home » Math » Geometry » 3D Geometry » Frustum of Cone » Volume of Frustum of Cone » Volume of Frustum of Cone given Slant Height, Height and Top Radius

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Created by Dhruv Walia

Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

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< Volume of Frustum of Cone Calculators

Volume of Frustum of Cone given Slant Height, Base Area and Top Area

LaTeX Go Volume of Frustum of Cone = (pi*sqrt(Slant Height of Frustum of Cone^2-(sqrt(Top Area of Frustum of Cone/pi)-sqrt(Base Area of Frustum of Cone/pi))^2))/3*(Top Area of Frustum of Cone/pi+Base Area of Frustum of Cone/pi+(sqrt(Top Area of Frustum of Cone/pi)*sqrt(Base Area of Frustum of Cone/pi)))

Volume of Frustum of Cone given Slant Height and Base Area

LaTeX Go Volume of Frustum of Cone = (pi*sqrt(Slant Height of Frustum of Cone^2-(Top Radius of Frustum of Cone-sqrt(Base Area of Frustum of Cone/pi))^2))/3*(Top Radius of Frustum of Cone^2+Base Area of Frustum of Cone/pi+(Top Radius of Frustum of Cone*sqrt(Base Area of Frustum of Cone/pi)))

Volume of Frustum of Cone given Slant Height and Top Area

LaTeX Go Volume of Frustum of Cone = (pi*sqrt(Slant Height of Frustum of Cone^2-(sqrt(Top Area of Frustum of Cone/pi)-Base Radius of Frustum of Cone)^2))/3*(Top Area of Frustum of Cone/pi+Base Radius of Frustum of Cone^2+(sqrt(Top Area of Frustum of Cone/pi)*Base Radius of Frustum of Cone))

Volume of Frustum of Cone given Top Area

LaTeX Go Volume of Frustum of Cone = 1/3*pi*Height of Frustum of Cone*(Top Area of Frustum of Cone/pi+Base Radius of Frustum of Cone^2+(sqrt(Top Area of Frustum of Cone/pi)*Base Radius of Frustum of Cone))

Volume of Frustum of Cone given Slant Height, Height and Top Radius Formula

LaTeX Go

What is a Frustum of Cone?

A Frustum of Cone is the part of cone when it is cut by a (horizontally parallel to the base) plane into two parts. The upper part of the cone remains same in shape but the bottom part makes a frustum.

How to Calculate Volume of Frustum of Cone given Slant Height, Height and Top Radius?

Volume of Frustum of Cone given Slant Height, Height and Top Radius calculator uses Volume of Frustum of Cone = 1/3*pi*Height of Frustum of Cone*(Top Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))^2+(Top Radius of Frustum of Cone*(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)))) to calculate the Volume of Frustum of Cone, The Volume of Frustum of Cone given Slant Height, Height and Top Radius formula is defined as the quantity of three dimensional space enclosed by the entire surface of Frustum of Cone, calculated using the slant height, top radius and height of the Frustum of Cone. Volume of Frustum of Cone is denoted by V symbol.

How to calculate Volume of Frustum of Cone given Slant Height, Height and Top Radius using this online calculator? To use this online calculator for Volume of Frustum of Cone given Slant Height, Height and Top Radius, enter Height of Frustum of Cone (h), Top Radius of Frustum of Cone (r_Top) & Slant Height of Frustum of Cone (h_Slant) and hit the calculate button. Here is how the Volume of Frustum of Cone given Slant Height, Height and Top Radius calculation can be explained with given input values -> 1619.444 = 1/3*pi*8*(10^2+(10-sqrt(9^2-8^2))^2+(10*(10-sqrt(9^2-8^2)))).

FAQ

What is Volume of Frustum of Cone given Slant Height, Height and Top Radius?

The Volume of Frustum of Cone given Slant Height, Height and Top Radius formula is defined as the quantity of three dimensional space enclosed by the entire surface of Frustum of Cone, calculated using the slant height, top radius and height of the Frustum of Cone and is represented as V = 1/3*pi*h*(r_Top^2+(r_Top-sqrt(h_Slant^2-h^2))^2+(r_Top*(r_Top-sqrt(h_Slant^2-h^2)))) or Volume of Frustum of Cone = 1/3*pi*Height of Frustum of Cone*(Top Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))^2+(Top Radius of Frustum of Cone*(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)))). Height of Frustum of Cone is the maximum vertical distance from the bottom to the top circular face of the Frustum of the Cone, Top Radius of Frustum of Cone is the distance between the center and any point on the circumference of the top circular surface of the Frustum of the Cone & The Slant Height of Frustum of Cone is the length of the line segment joining the extremities of two parallel radii, drawn in the same direction of the two circular bases.

How to calculate Volume of Frustum of Cone given Slant Height, Height and Top Radius?

The Volume of Frustum of Cone given Slant Height, Height and Top Radius formula is defined as the quantity of three dimensional space enclosed by the entire surface of Frustum of Cone, calculated using the slant height, top radius and height of the Frustum of Cone is calculated using Volume of Frustum of Cone = 1/3*pi*Height of Frustum of Cone*(Top Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))^2+(Top Radius of Frustum of Cone*(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)))). To calculate Volume of Frustum of Cone given Slant Height, Height and Top Radius, you need Height of Frustum of Cone (h), Top Radius of Frustum of Cone (r_Top) & Slant Height of Frustum of Cone (h_Slant). With our tool, you need to enter the respective value for Height of Frustum of Cone, Top Radius of Frustum of Cone & Slant Height of Frustum of Cone and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Volume of Frustum of Cone?

In this formula, Volume of Frustum of Cone uses Height of Frustum of Cone, Top Radius of Frustum of Cone & Slant Height of Frustum of Cone. We can use 3 other way(s) to calculate the same, which is/are as follows -

Volume of Frustum of Cone = (pi*sqrt(Slant Height of Frustum of Cone^2-(Top Radius of Frustum of Cone-sqrt(Base Area of Frustum of Cone/pi))^2))/3*(Top Radius of Frustum of Cone^2+Base Area of Frustum of Cone/pi+(Top Radius of Frustum of Cone*sqrt(Base Area of Frustum of Cone/pi)))
Volume of Frustum of Cone = (pi*sqrt(Slant Height of Frustum of Cone^2-(sqrt(Top Area of Frustum of Cone/pi)-sqrt(Base Area of Frustum of Cone/pi))^2))/3*(Top Area of Frustum of Cone/pi+Base Area of Frustum of Cone/pi+(sqrt(Top Area of Frustum of Cone/pi)*sqrt(Base Area of Frustum of Cone/pi)))
Volume of Frustum of Cone = (pi*sqrt(Slant Height of Frustum of Cone^2-(sqrt(Top Area of Frustum of Cone/pi)-Base Radius of Frustum of Cone)^2))/3*(Top Area of Frustum of Cone/pi+Base Radius of Frustum of Cone^2+(sqrt(Top Area of Frustum of Cone/pi)*Base Radius of Frustum of Cone))

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