Slant Height of Frustum of Cone given Volume Solution

STEP 0: Pre-Calculation Summary
Formula Used
Slant Height of Frustum of Cone = sqrt(((3*Volume of Frustum of Cone)/(pi*(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone*Base Radius of Frustum of Cone))))^2+(Top Radius of Frustum of Cone-Base Radius of Frustum of Cone)^2)
hSlant = sqrt(((3*V)/(pi*(rTop^2+rBase^2+(rTop*rBase))))^2+(rTop-rBase)^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 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.
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 Radius of Frustum of Cone: 10 Meter --> 10 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
hSlant = sqrt(((3*V)/(pi*(rTop^2+rBase^2+(rTop*rBase))))^2+(rTop-rBase)^2) --> sqrt(((3*1500)/(pi*(10^2+5^2+(10*5))))^2+(10-5)^2)
Evaluating ... ...
hSlant = 9.59145703005666
STEP 3: Convert Result to Output's Unit
9.59145703005666 Meter --> No Conversion Required
FINAL ANSWER
9.59145703005666 9.591457 Meter <-- Slant Height of Frustum of Cone
(Calculation completed in 00.020 seconds)

Credits

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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 Calculators

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

Slant Height of Frustum of Cone given Volume Formula

​LaTeX ​Go
Slant Height of Frustum of Cone = sqrt(((3*Volume of Frustum of Cone)/(pi*(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone*Base Radius of Frustum of Cone))))^2+(Top Radius of Frustum of Cone-Base Radius of Frustum of Cone)^2)
hSlant = sqrt(((3*V)/(pi*(rTop^2+rBase^2+(rTop*rBase))))^2+(rTop-rBase)^2)

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?

Slant Height of Frustum of Cone given Volume calculator uses Slant Height of Frustum of Cone = sqrt(((3*Volume of Frustum of Cone)/(pi*(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone*Base Radius of Frustum of Cone))))^2+(Top Radius of Frustum of Cone-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 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 of Frustum of Cone. Slant Height of Frustum of Cone is denoted by hSlant symbol.

How to calculate Slant Height of Frustum of Cone given Volume using this online calculator? To use this online calculator for Slant Height of Frustum of Cone given Volume, enter Volume of Frustum of Cone (V), Top Radius of Frustum of Cone (rTop) & Base Radius of Frustum of Cone (rBase) and hit the calculate button. Here is how the Slant Height of Frustum of Cone given Volume calculation can be explained with given input values -> 9.591457 = sqrt(((3*1500)/(pi*(10^2+5^2+(10*5))))^2+(10-5)^2).

FAQ

What is Slant Height of Frustum of Cone given Volume?
The Slant Height of Frustum of Cone given Volume 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 of Frustum of Cone and is represented as hSlant = sqrt(((3*V)/(pi*(rTop^2+rBase^2+(rTop*rBase))))^2+(rTop-rBase)^2) or Slant Height of Frustum of Cone = sqrt(((3*Volume of Frustum of Cone)/(pi*(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone*Base Radius of Frustum of Cone))))^2+(Top Radius of Frustum of Cone-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 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 & 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?
The Slant Height of Frustum of Cone given Volume 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 of Frustum of Cone is calculated using Slant Height of Frustum of Cone = sqrt(((3*Volume of Frustum of Cone)/(pi*(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone*Base Radius of Frustum of Cone))))^2+(Top Radius of Frustum of Cone-Base Radius of Frustum of Cone)^2). To calculate Slant Height of Frustum of Cone given Volume, you need Volume of Frustum of Cone (V), Top Radius of Frustum of Cone (rTop) & Base Radius of Frustum of Cone (rBase). With our tool, you need to enter the respective value for Volume of Frustum of Cone, Top Radius 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 Radius 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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