Volume of Frustum of Cone given Curved Surface Area and Top Area Calculator

✖Curved Surface Area of Frustum of Cone is the quantity of plane enclosed by curved surfaces (that is, top and bottom faces are excluded) of the Frustum of the Cone.ⓘ Curved Surface Area of Frustum of Cone [CSA]			+10% -10%
✖Top Area of Frustum of Cone is the total amount of two-dimensional space occupied by the top face of the Frustum of the Cone.ⓘ Top Area of Frustum of Cone [A_Top]			+10% -10%
✖Base Radius of Frustum of Cone is the distance between the center and any point on the circumference of the base circular surface of the Frustum of the Cone.ⓘ Base Radius of Frustum of Cone [r_Base]			+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 Curved Surface Area and Top Area [V]

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Volume of Frustum of Cone given Curved Surface Area and Top Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Frustum of Cone = 1/3*pi*sqrt((Curved Surface Area of Frustum of Cone/(pi*(sqrt(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)^2)*(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))
V = 1/3*pi*sqrt((CSA/(pi*(sqrt(A_Top/pi)+r_Base)))^2-(sqrt(A_Top/pi)-r_Base)^2)*(A_Top/pi+r_Base^2+(sqrt(A_Top/pi)*r_Base))
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.
Curved Surface Area of Frustum of Cone - (Measured in Square Meter) - Curved Surface Area of Frustum of Cone is the quantity of plane enclosed by curved surfaces (that is, top and bottom faces are excluded) of the Frustum of the Cone.
Top Area of Frustum of Cone - (Measured in Square Meter) - Top Area of Frustum of Cone is the total amount of two-dimensional space occupied by the top face of the Frustum of the Cone.
Base Radius of Frustum of Cone - (Measured in Meter) - Base Radius of Frustum of Cone is the distance between the center and any point on the circumference of the base circular surface of the Frustum of the Cone.

STEP 1: Convert Input(s) to Base Unit

Curved Surface Area of Frustum of Cone: 450 Square Meter --> 450 Square Meter No Conversion Required
Top Area of Frustum of Cone: 315 Square Meter --> 315 Square Meter No Conversion Required
Base Radius of Frustum of Cone: 5 Meter --> 5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = 1/3*pi*sqrt((CSA/(pi*(sqrt(A_Top/pi)+r_Base)))^2-(sqrt(A_Top/pi)-r_Base)^2)*(A_Top/pi+r_Base^2+(sqrt(A_Top/pi)*r_Base)) --> 1/3*pi*sqrt((450/(pi*(sqrt(315/pi)+5)))^2-(sqrt(315/pi)-5)^2)*(315/pi+5^2+(sqrt(315/pi)*5))

Evaluating ... ...

V = 1490.44147459514

STEP 3: Convert Result to Output's Unit

1490.44147459514 Cubic Meter --> No Conversion Required

FINAL ANSWER

1490.44147459514 ≈ 1490.441 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 Curved Surface Area and Top Area

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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 Curved Surface Area and Top Area 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 Curved Surface Area and Top Area?

Volume of Frustum of Cone given Curved Surface Area and Top Area calculator uses Volume of Frustum of Cone = 1/3*pi*sqrt((Curved Surface Area of Frustum of Cone/(pi*(sqrt(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)^2)*(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)) to calculate the Volume of Frustum of Cone, The Volume of Frustum of Cone given Curved Surface Area and Top Area formula is defined as the quantity of three dimensional space enclosed by the entire surface of Frustum of Cone, calculated using the curved surface area, top area and base radius of the Frustum of Cone. Volume of Frustum of Cone is denoted by V symbol.

How to calculate Volume of Frustum of Cone given Curved Surface Area and Top Area using this online calculator? To use this online calculator for Volume of Frustum of Cone given Curved Surface Area and Top Area, enter Curved Surface Area of Frustum of Cone (CSA), Top Area of Frustum of Cone (A_Top) & Base Radius of Frustum of Cone (r_Base) and hit the calculate button. Here is how the Volume of Frustum of Cone given Curved Surface Area and Top Area calculation can be explained with given input values -> 1490.441 = 1/3*pi*sqrt((450/(pi*(sqrt(315/pi)+5)))^2-(sqrt(315/pi)-5)^2)*(315/pi+5^2+(sqrt(315/pi)*5)).

FAQ

What is Volume of Frustum of Cone given Curved Surface Area and Top Area?

The Volume of Frustum of Cone given Curved Surface Area and Top Area formula is defined as the quantity of three dimensional space enclosed by the entire surface of Frustum of Cone, calculated using the curved surface area, top area and base radius of the Frustum of Cone and is represented as V = 1/3*pi*sqrt((CSA/(pi*(sqrt(A_Top/pi)+r_Base)))^2-(sqrt(A_Top/pi)-r_Base)^2)*(A_Top/pi+r_Base^2+(sqrt(A_Top/pi)*r_Base)) or Volume of Frustum of Cone = 1/3*pi*sqrt((Curved Surface Area of Frustum of Cone/(pi*(sqrt(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)^2)*(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)). Curved Surface Area of Frustum of Cone is the quantity of plane enclosed by curved surfaces (that is, top and bottom faces are excluded) of the Frustum of the Cone, Top Area of Frustum of Cone is the total amount of two-dimensional space occupied by the top face of the Frustum of the Cone & Base Radius of Frustum of Cone is the distance between the center and any point on the circumference of the base circular surface of the Frustum of the Cone.

How to calculate Volume of Frustum of Cone given Curved Surface Area and Top Area?

The Volume of Frustum of Cone given Curved Surface Area and Top Area formula is defined as the quantity of three dimensional space enclosed by the entire surface of Frustum of Cone, calculated using the curved surface area, top area and base radius of the Frustum of Cone is calculated using Volume of Frustum of Cone = 1/3*pi*sqrt((Curved Surface Area of Frustum of Cone/(pi*(sqrt(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)^2)*(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)). To calculate Volume of Frustum of Cone given Curved Surface Area and Top Area, you need Curved Surface Area of Frustum of Cone (CSA), Top Area of Frustum of Cone (A_Top) & Base Radius of Frustum of Cone (r_Base). With our tool, you need to enter the respective value for Curved Surface Area of Frustum of Cone, Top Area of Frustum of Cone & Base Radius 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 Curved Surface Area of Frustum of Cone, Top Area of Frustum of Cone & Base Radius 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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