Slant Height of Frustum of Cone given Volume and Top Area Calculator

✖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 [V]			+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%

✖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 given Volume and Top Area [h_Slant]

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Slant Height of Frustum of Cone given Volume and Top Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.
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

Volume of Frustum of Cone: 1500 Cubic Meter --> 1500 Cubic 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

h_Slant = sqrt(((3*V)/(pi*(A_Top/pi+r_Base^2+(sqrt(A_Top/pi)*r_Base))))^2+(sqrt(A_Top/pi)-r_Base)^2) --> sqrt(((3*1500)/(pi*(315/pi+5^2+(sqrt(315/pi)*5))))^2+(sqrt(315/pi)-5)^2)

Evaluating ... ...

h_Slant = 9.58512290674049

STEP 3: Convert Result to Output's Unit

9.58512290674049 Meter --> No Conversion Required

FINAL ANSWER

9.58512290674049 ≈ 9.585123 Meter <-- Slant Height of Frustum of Cone

(Calculation completed in 00.004 seconds)

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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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Institute of Chartered and Financial Analysts of India National college (ICFAI National College), HUBLI

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< Slant Height of Frustum of Cone Calculators

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

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

Slant Height of Frustum of Cone given Curved Surface Area and Base Area

LaTeX Go Slant Height of Frustum of Cone = Curved Surface Area of Frustum of Cone/(pi*(Top Radius of Frustum of Cone+sqrt(Base Area of Frustum of Cone/pi)))

Slant Height of Frustum of Cone given Base Area

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

Slant Height of Frustum of Cone given Top Area

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

Slant Height of Frustum of Cone given Volume 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 Slant Height of Frustum of Cone given Volume and Top Area?

Slant Height of Frustum of Cone given Volume and Top Area calculator uses Slant Height of Frustum of Cone = sqrt(((3*Volume of Frustum of Cone)/(pi*(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+(sqrt(Top Area of Frustum of Cone/pi)-Base Radius of Frustum of Cone)^2) to calculate the Slant Height of Frustum of Cone, The Slant Height of Frustum of Cone given Volume and Top Area formula is defined as the length of the line segment joining the extremities of two parallel radii, drawn in the same direction of the two circular bases of Frustum of Cone, calculated using volume, base radius and top area of Frustum of Cone. Slant Height of Frustum of Cone is denoted by h_Slant symbol.

How to calculate Slant Height of Frustum of Cone given Volume and Top Area using this online calculator? To use this online calculator for Slant Height of Frustum of Cone given Volume and Top Area, enter Volume of Frustum of Cone (V), 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 Slant Height of Frustum of Cone given Volume and Top Area calculation can be explained with given input values -> 9.585123 = sqrt(((3*1500)/(pi*(315/pi+5^2+(sqrt(315/pi)*5))))^2+(sqrt(315/pi)-5)^2).

FAQ

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

The Slant Height of Frustum of Cone given Volume and Top Area formula is defined as the length of the line segment joining the extremities of two parallel radii, drawn in the same direction of the two circular bases of Frustum of Cone, calculated using volume, base radius and top area of Frustum of Cone and is represented as h_Slant = sqrt(((3*V)/(pi*(A_Top/pi+r_Base^2+(sqrt(A_Top/pi)*r_Base))))^2+(sqrt(A_Top/pi)-r_Base)^2) or Slant Height of Frustum of Cone = sqrt(((3*Volume of Frustum of Cone)/(pi*(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+(sqrt(Top Area of Frustum of Cone/pi)-Base Radius of Frustum of Cone)^2). Volume of Frustum of Cone is the quantity of three-dimensional space enclosed by the entire surface 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 Slant Height of Frustum of Cone given Volume and Top Area?

The Slant Height of Frustum of Cone given Volume and Top Area formula is defined as the length of the line segment joining the extremities of two parallel radii, drawn in the same direction of the two circular bases of Frustum of Cone, calculated using volume, base radius and top area of Frustum of Cone is calculated using Slant Height of Frustum of Cone = sqrt(((3*Volume of Frustum of Cone)/(pi*(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+(sqrt(Top Area of Frustum of Cone/pi)-Base Radius of Frustum of Cone)^2). To calculate Slant Height of Frustum of Cone given Volume and Top Area, you need Volume of Frustum of Cone (V), 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 Volume 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 Slant Height of Frustum of Cone?

In this formula, Slant Height of Frustum of Cone uses Volume 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 -

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

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