Total Surface Area of Frustum of Cone given Slant Height, Height and Top Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Total Surface Area of Frustum of Cone = pi*(((2*Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))*Slant 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)
TSA = pi*(((2*rTop-sqrt(hSlant^2-h^2))*hSlant)+rTop^2+(rTop-sqrt(hSlant^2-h^2))^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
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.
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.
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.
STEP 1: Convert Input(s) to Base Unit
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
Height of Frustum of Cone: 8 Meter --> 8 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
TSA = pi*(((2*rTop-sqrt(hSlant^2-h^2))*hSlant)+rTop^2+(rTop-sqrt(hSlant^2-h^2))^2) --> pi*(((2*10-sqrt(9^2-8^2))*9)+10^2+(10-sqrt(9^2-8^2))^2)
Evaluating ... ...
TSA = 871.571851516107
STEP 3: Convert Result to Output's Unit
871.571851516107 Square Meter --> No Conversion Required
FINAL ANSWER
871.571851516107 871.5719 Square Meter <-- Total Surface Area of Frustum of Cone
(Calculation completed in 00.004 seconds)

Credits

Created by Dhruv Walia
Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
Dhruv Walia has created this Calculator and 1100+ more calculators!
Verified by Nayana Phulphagar
Institute of Chartered and Financial Analysts of India National college (ICFAI National College), HUBLI
Nayana Phulphagar has verified this Calculator and 1400+ more calculators!

20 Total Surface Area of Frustum of Cone Calculators

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

Total Surface Area of Frustum of Cone given Slant Height, Height and Top Radius Formula

Total Surface Area of Frustum of Cone = pi*(((2*Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))*Slant 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)
TSA = pi*(((2*rTop-sqrt(hSlant^2-h^2))*hSlant)+rTop^2+(rTop-sqrt(hSlant^2-h^2))^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 Total Surface Area of Frustum of Cone given Slant Height, Height and Top Radius?

Total Surface Area of Frustum of Cone given Slant Height, Height and Top Radius calculator uses Total Surface Area of Frustum of Cone = pi*(((2*Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))*Slant 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) to calculate the Total Surface Area of Frustum of Cone, The Total Surface Area of Frustum of Cone given Slant Height, Height and Top Radius formula is defined as the total quantity of plane enclosed on the entire surface of the Frustum of Cone, calculated using the slant height, top radius and height of the Frustum of Cone. Total Surface Area of Frustum of Cone is denoted by TSA symbol.

How to calculate Total Surface Area of Frustum of Cone given Slant Height, Height and Top Radius using this online calculator? To use this online calculator for Total Surface Area of Frustum of Cone given Slant Height, Height and Top Radius, enter Top Radius of Frustum of Cone (rTop), Slant Height of Frustum of Cone (hSlant) & Height of Frustum of Cone (h) and hit the calculate button. Here is how the Total Surface Area of Frustum of Cone given Slant Height, Height and Top Radius calculation can be explained with given input values -> 871.5719 = pi*(((2*10-sqrt(9^2-8^2))*9)+10^2+(10-sqrt(9^2-8^2))^2).

FAQ

What is Total Surface Area of Frustum of Cone given Slant Height, Height and Top Radius?
The Total Surface Area of Frustum of Cone given Slant Height, Height and Top Radius formula is defined as the total quantity of plane enclosed on the entire surface of the Frustum of Cone, calculated using the slant height, top radius and height of the Frustum of Cone and is represented as TSA = pi*(((2*rTop-sqrt(hSlant^2-h^2))*hSlant)+rTop^2+(rTop-sqrt(hSlant^2-h^2))^2) or Total Surface Area of Frustum of Cone = pi*(((2*Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))*Slant 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 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 & Height of Frustum of Cone is the maximum vertical distance from the bottom to the top circular face of the Frustum of the Cone.
How to calculate Total Surface Area of Frustum of Cone given Slant Height, Height and Top Radius?
The Total Surface Area of Frustum of Cone given Slant Height, Height and Top Radius formula is defined as the total quantity of plane enclosed on the entire surface of the Frustum of Cone, calculated using the slant height, top radius and height of the Frustum of Cone is calculated using Total Surface Area of Frustum of Cone = pi*(((2*Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))*Slant 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). To calculate Total Surface Area of Frustum of Cone given Slant Height, Height and Top Radius, you need Top Radius of Frustum of Cone (rTop), Slant Height of Frustum of Cone (hSlant) & Height of Frustum of Cone (h). With our tool, you need to enter the respective value for Top Radius of Frustum of Cone, Slant Height of Frustum of Cone & 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 Total Surface Area of Frustum of Cone?
In this formula, Total Surface Area of Frustum of Cone uses Top Radius of Frustum of Cone, Slant Height of Frustum of Cone & Height of Frustum of Cone. We can use 19 other way(s) to calculate the same, which is/are as follows -
  • Total 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)+Top Area of Frustum of Cone+Base Area of Frustum of Cone
  • Total Surface Area of Frustum of Cone = pi*(((sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)+2*sqrt(Base Area of Frustum of Cone/pi))*Slant Height of Frustum of Cone)+(sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)+sqrt(Base Area of Frustum of Cone/pi))^2)+Base Area of Frustum of Cone
  • Total Surface Area of Frustum of Cone = pi*(((sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)+2*Base Radius of Frustum of Cone)*Slant Height of Frustum of Cone)+(sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)+Base Radius of Frustum of Cone)^2+Base Radius of Frustum of Cone^2)
  • Total Surface Area of Frustum of Cone = pi*(((2*sqrt(Top Area of Frustum of Cone/pi)-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))*Slant Height of Frustum of Cone)+(sqrt(Top Area of Frustum of Cone/pi)-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))^2)+Top Area of Frustum of Cone
  • Total Surface Area of Frustum of Cone = pi*(((Top Radius of Frustum of Cone+sqrt(Base Area of Frustum of Cone/pi))*sqrt((Top Radius of Frustum of Cone-sqrt(Base Area of Frustum of Cone/pi))^2+Height of Frustum of Cone^2))+Top Radius of Frustum of Cone^2)+Base Area of Frustum of Cone
  • Total Surface Area of Frustum of Cone = pi*((sqrt(Top Area of Frustum of Cone/pi)+sqrt(Base Area of Frustum of Cone/pi))*sqrt((sqrt(Top Area of Frustum of Cone/pi)-sqrt(Base Area of Frustum of Cone/pi))^2+Height of Frustum of Cone^2))+Top Area of Frustum of Cone+Base Area of Frustum of Cone
  • Total Surface Area of Frustum of Cone = pi*(((sqrt(Top Area of Frustum of Cone/pi)+Base Radius of Frustum of Cone)*sqrt((sqrt(Top Area of Frustum of Cone/pi)-Base Radius of Frustum of Cone)^2+Height of Frustum of Cone^2))+Base Radius of Frustum of Cone^2)+Top Area of Frustum of Cone
  • Total 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)+Top Radius of Frustum of Cone^2+Base Area of Frustum of Cone/pi)
  • Total 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)+Top Area of Frustum of Cone/pi+Base Radius of Frustum of Cone^2)
  • Total Surface Area of Frustum of Cone = Curved Surface Area of Frustum of Cone+(pi*Base Radius of Frustum of Cone^2)+Top Area of Frustum of Cone
  • Total Surface Area of Frustum of Cone = Curved Surface Area of Frustum of Cone+(pi*Top Radius of Frustum of Cone^2)+Base Area of Frustum of Cone
  • Total Surface Area of Frustum of Cone = Curved Surface Area of Frustum of Cone+Base Area of Frustum of Cone+Top Area of Frustum of Cone
  • Total Surface Area of Frustum of Cone = pi*(((Top Radius of Frustum of Cone+sqrt(Base Area of Frustum of Cone/pi))*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))+Top Radius of Frustum of Cone^2+Base Area of Frustum of Cone/pi)
  • Total Surface Area of Frustum of Cone = pi*(((sqrt(Top Area of Frustum of Cone/pi)+Base Radius 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))+Top Area of Frustum of Cone/pi+Base Radius of Frustum of Cone^2)
  • Total Surface Area of Frustum of Cone = (pi*(sqrt(Top Area of Frustum of Cone/pi)+sqrt(Base Area of Frustum of Cone/pi))*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))+Top Area of Frustum of Cone+Base Area of Frustum of Cone
  • Total Surface Area of Frustum of Cone = pi*(((Top Radius of Frustum of Cone+Base Radius of Frustum of Cone)*sqrt((Top Radius of Frustum of Cone-Base Radius of Frustum of Cone)^2+Height of Frustum of Cone^2))+Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2)
  • Total Surface Area of Frustum of Cone = Curved Surface Area of Frustum of Cone+(pi*(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2))
  • Total 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)+Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2)
  • Total Surface Area of Frustum of Cone = pi*(((Top Radius of Frustum of Cone+Base Radius 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))+Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2)
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!