Slant Height of Frustum of Cone given Total Surface Area Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
hSlant = (TSA/pi-(rTop^2+rBase^2))/(rTop+rBase)
This formula uses 1 Constants, 4 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
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.
Total Surface Area of Frustum of Cone - (Measured in Square Meter) - Total Surface Area of Frustum of Cone is the total quantity of plane enclosed on 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
Total Surface Area of Frustum of Cone: 850 Square Meter --> 850 Square 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 = (TSA/pi-(rTop^2+rBase^2))/(rTop+rBase) --> (850/pi-(10^2+5^2))/(10+5)
Evaluating ... ...
hSlant = 9.70422688374814
STEP 3: Convert Result to Output's Unit
9.70422688374814 Meter --> No Conversion Required
FINAL ANSWER
9.70422688374814 9.704227 Meter <-- Slant Height of Frustum of Cone
(Calculation completed in 00.004 seconds)

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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
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16 Slant Height of Frustum of Cone Calculators

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

4 Slant Height of Frustum of Cone Calculators

Slant Height of Frustum of Cone given Volume
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
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
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
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 Total Surface Area Formula

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)
hSlant = (TSA/pi-(rTop^2+rBase^2))/(rTop+rBase)

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 Total Surface Area?

Slant Height of Frustum of Cone given Total Surface Area calculator uses 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) to calculate the Slant Height of Frustum of Cone, The Slant Height of Frustum of Cone given Total Surface 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 total surface area 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 Total Surface Area using this online calculator? To use this online calculator for Slant Height of Frustum of Cone given Total Surface Area, enter Total Surface Area of Frustum of Cone (TSA), 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 Total Surface Area calculation can be explained with given input values -> 9.704227 = (850/pi-(10^2+5^2))/(10+5).

FAQ

What is Slant Height of Frustum of Cone given Total Surface Area?
The Slant Height of Frustum of Cone given Total Surface 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 total surface area of Frustum of Cone and is represented as hSlant = (TSA/pi-(rTop^2+rBase^2))/(rTop+rBase) or 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). Total Surface Area of Frustum of Cone is the total quantity of plane enclosed on 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 Total Surface Area?
The Slant Height of Frustum of Cone given Total Surface 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 total surface area of Frustum of Cone is calculated using 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). To calculate Slant Height of Frustum of Cone given Total Surface Area, you need Total Surface Area of Frustum of Cone (TSA), 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 Total Surface Area 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 Total Surface Area of Frustum of Cone, Top Radius of Frustum of Cone & Base Radius of Frustum of Cone. We can use 18 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)
  • 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 = Curved Surface Area of Frustum of Cone/(pi*(sqrt(Top Area of Frustum of Cone/pi)+sqrt(Base Area of Frustum of Cone/pi)))
  • Slant Height of Frustum of Cone = Curved Surface Area of Frustum of Cone/(pi*(sqrt(Top Area of Frustum of Cone/pi)+Base Radius of Frustum of Cone))
  • Slant Height of Frustum of Cone = (Total Surface Area 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)
  • Slant Height of Frustum of Cone = (Total Surface Area of Frustum of Cone/pi-(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))
  • Slant Height of Frustum of Cone = (Total Surface Area of Frustum of Cone/pi-(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))
  • 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)
  • Slant Height of Frustum of Cone = sqrt(((3*Volume of Frustum of Cone)/(pi*(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)))))^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(((3*Volume of Frustum of Cone)/(pi*(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)))))^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+(Top Radius of Frustum of Cone-Base Radius of Frustum of Cone)^2)
  • 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 = 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 = 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 = 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 = 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)
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