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

✖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%
✖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 [h_Slant]			+10% -10%
✖Height of Frustum of Cone is the maximum vertical distance from the bottom to the top circular face of the Frustum of the Cone.ⓘ Height of Frustum of Cone [h]			+10% -10%

✖Total Surface Area of Frustum of Cone is the total quantity of plane enclosed on the entire surface of the Frustum of the Cone.ⓘ Total Surface Area of Frustum of Cone given Slant Height, Height and Top Area [TSA]

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

STEP 0: Pre-Calculation Summary

Formula Used

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
TSA = pi*(((2*sqrt(A_Top/pi)-sqrt(h_Slant^2-h^2))*h_Slant)+(sqrt(A_Top/pi)-sqrt(h_Slant^2-h^2))^2)+A_Top
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 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.
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 Area of Frustum of Cone: 315 Square Meter --> 315 Square 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*sqrt(A_Top/pi)-sqrt(h_Slant^2-h^2))*h_Slant)+(sqrt(A_Top/pi)-sqrt(h_Slant^2-h^2))^2)+A_Top --> pi*(((2*sqrt(315/pi)-sqrt(9^2-8^2))*9)+(sqrt(315/pi)-sqrt(9^2-8^2))^2)+315

Evaluating ... ...

TSA = 873.663064252559

STEP 3: Convert Result to Output's Unit

873.663064252559 Square Meter --> No Conversion Required

FINAL ANSWER

873.663064252559 ≈ 873.6631 Square Meter <-- Total Surface Area of Frustum of Cone

(Calculation completed in 00.020 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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< Total Surface Area of Frustum of Cone Calculators

Total Surface Area of Frustum of Cone given Slant Height, Height and Base Area

LaTeX 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 Base Radius

LaTeX 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

LaTeX 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 given Slant Height, Base Area and Top Area

LaTeX 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, Height 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 Total Surface Area of Frustum of Cone given Slant Height, Height and Top Area?

Total Surface Area of Frustum of Cone given Slant Height, Height and Top Area calculator uses 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 to calculate the Total Surface Area of Frustum of Cone, The Total Surface Area of Frustum of Cone given Slant Height, Height and Top Area 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 area 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 Area using this online calculator? To use this online calculator for Total Surface Area of Frustum of Cone given Slant Height, Height and Top Area, enter Top Area of Frustum of Cone (A_Top), Slant Height of Frustum of Cone (h_Slant) & 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 Area calculation can be explained with given input values -> 873.6631 = pi*(((2*sqrt(315/pi)-sqrt(9^2-8^2))*9)+(sqrt(315/pi)-sqrt(9^2-8^2))^2)+315.

FAQ

What is Total Surface Area of Frustum of Cone given Slant Height, Height and Top Area?

The Total Surface Area of Frustum of Cone given Slant Height, Height and Top Area 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 area and height of the Frustum of Cone and is represented as TSA = pi*(((2*sqrt(A_Top/pi)-sqrt(h_Slant^2-h^2))*h_Slant)+(sqrt(A_Top/pi)-sqrt(h_Slant^2-h^2))^2)+A_Top or 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. 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, 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 Area?

The Total Surface Area of Frustum of Cone given Slant Height, Height and Top Area 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 area and height of the Frustum of Cone is calculated using 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. To calculate Total Surface Area of Frustum of Cone given Slant Height, Height and Top Area, you need Top Area of Frustum of Cone (A_Top), Slant Height of Frustum of Cone (h_Slant) & Height of Frustum of Cone (h). With our tool, you need to enter the respective value for Top Area 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 Area of Frustum of Cone, Slant Height of Frustum of Cone & Height of Frustum of Cone. We can use 3 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)

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