Total Surface Area of Hollow Frustum Calculator

✖Number of Base Vertices of Hollow Frustum is the number of vertices of the base polygon of the Hollow Frustum.ⓘ Number of Base Vertices of Hollow Frustum [n]			+10% -10%
✖Long Outer Side of Hollow Frustum is the side length of the outer regular polygon on the base of the Hollow Frustum.ⓘ Long Outer Side of Hollow Frustum [S_{Long Outer}]			+10% -10%
✖Short Outer Side of Hollow Frustum is the side length of the outer regular polygon on the top of the Hollow Frustum.ⓘ Short Outer Side of Hollow Frustum [S_{Short Outer}]			+10% -10%
✖Height of Hollow Frustum is the maximum vertical distance from the bottom to top of the Hollow Frustum.ⓘ Height of Hollow Frustum [h]			+10% -10%
✖Long Inner Side of Hollow Frustum is the side length of the inner regular polygon on the base of the Hollow Frustum.ⓘ Long Inner Side of Hollow Frustum [S_{Long Inner}]			+10% -10%
✖Short Inner Side of Hollow Frustum is the side length of the inner regular polygon on the top of the Hollow Frustum.ⓘ Short Inner Side of Hollow Frustum [S_{Short Inner}]			+10% -10%

✖Total Surface Area of Hollow Frustum is the total quantity of plane occupied by the surface of the entire Hollow Frustum.ⓘ Total Surface Area of Hollow Frustum [TSA]

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Total Surface Area of Hollow Frustum Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Hollow Frustum = (Number of Base Vertices of Hollow Frustum/4*(Long Outer Side of Hollow Frustum+Short Outer Side of Hollow Frustum)*sqrt(((cot(pi/Number of Base Vertices of Hollow Frustum))^2*(Long Outer Side of Hollow Frustum-Short Outer Side of Hollow Frustum)^2)+(4*Height of Hollow Frustum^2)))+(Number of Base Vertices of Hollow Frustum/4*(Long Inner Side of Hollow Frustum+Short Inner Side of Hollow Frustum)*sqrt(((cot(pi/Number of Base Vertices of Hollow Frustum))^2*(Long Inner Side of Hollow Frustum-Short Inner Side of Hollow Frustum)^2)+(4*Height of Hollow Frustum^2)))+((Number of Base Vertices of Hollow Frustum*(Long Outer Side of Hollow Frustum^2-Long Inner Side of Hollow Frustum^2))/(4*tan(pi/Number of Base Vertices of Hollow Frustum)))+((Number of Base Vertices of Hollow Frustum*(Short Outer Side of Hollow Frustum^2-Short Inner Side of Hollow Frustum^2))/(4*tan(pi/Number of Base Vertices of Hollow Frustum)))
TSA = (n/4*(S_{Long Outer}+S_{Short Outer})*sqrt(((cot(pi/n))^2*(S_{Long Outer}-S_{Short Outer})^2)+(4*h^2)))+(n/4*(S_{Long Inner}+S_{Short Inner})*sqrt(((cot(pi/n))^2*(S_{Long Inner}-S_{Short Inner})^2)+(4*h^2)))+((n*(S_{Long Outer}^2-S_{Long Inner}^2))/(4*tan(pi/n)))+((n*(S_{Short Outer}^2-S_{Short Inner}^2))/(4*tan(pi/n)))
This formula uses 1 Constants, 3 Functions, 7 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
cot - Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle., cot(Angle)
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 Hollow Frustum - (Measured in Square Meter) - Total Surface Area of Hollow Frustum is the total quantity of plane occupied by the surface of the entire Hollow Frustum.
Number of Base Vertices of Hollow Frustum - Number of Base Vertices of Hollow Frustum is the number of vertices of the base polygon of the Hollow Frustum.
Long Outer Side of Hollow Frustum - (Measured in Meter) - Long Outer Side of Hollow Frustum is the side length of the outer regular polygon on the base of the Hollow Frustum.
Short Outer Side of Hollow Frustum - (Measured in Meter) - Short Outer Side of Hollow Frustum is the side length of the outer regular polygon on the top of the Hollow Frustum.
Height of Hollow Frustum - (Measured in Meter) - Height of Hollow Frustum is the maximum vertical distance from the bottom to top of the Hollow Frustum.
Long Inner Side of Hollow Frustum - (Measured in Meter) - Long Inner Side of Hollow Frustum is the side length of the inner regular polygon on the base of the Hollow Frustum.
Short Inner Side of Hollow Frustum - (Measured in Meter) - Short Inner Side of Hollow Frustum is the side length of the inner regular polygon on the top of the Hollow Frustum.

STEP 1: Convert Input(s) to Base Unit

Number of Base Vertices of Hollow Frustum: 4 --> No Conversion Required
Long Outer Side of Hollow Frustum: 14 Meter --> 14 Meter No Conversion Required
Short Outer Side of Hollow Frustum: 9 Meter --> 9 Meter No Conversion Required
Height of Hollow Frustum: 6 Meter --> 6 Meter No Conversion Required
Long Inner Side of Hollow Frustum: 10 Meter --> 10 Meter No Conversion Required
Short Inner Side of Hollow Frustum: 5 Meter --> 5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = (n/4*(S_{Long Outer}+S_{Short Outer})*sqrt(((cot(pi/n))^2*(S_{Long Outer}-S_{Short Outer})^2)+(4*h^2)))+(n/4*(S_{Long Inner}+S_{Short Inner})*sqrt(((cot(pi/n))^2*(S_{Long Inner}-S_{Short Inner})^2)+(4*h^2)))+((n*(S_{Long Outer}^2-S_{Long Inner}^2))/(4*tan(pi/n)))+((n*(S_{Short Outer}^2-S_{Short Inner}^2))/(4*tan(pi/n))) --> (4/4*(14+9)*sqrt(((cot(pi/4))^2*(14-9)^2)+(4*6^2)))+(4/4*(10+5)*sqrt(((cot(pi/4))^2*(10-5)^2)+(4*6^2)))+((4*(14^2-10^2))/(4*tan(pi/4)))+((4*(9^2-5^2))/(4*tan(pi/4)))

Evaluating ... ...

TSA = 646

STEP 3: Convert Result to Output's Unit

646 Square Meter --> No Conversion Required

FINAL ANSWER

646 Square Meter <-- Total Surface Area of Hollow Frustum

(Calculation completed in 00.004 seconds)

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Walchand College of Engineering (WCE), Sangli

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< Surface Area of Hollow Frustum Calculators

Total Surface Area of Hollow Frustum

LaTeX Go Total Surface Area of Hollow Frustum = (Number of Base Vertices of Hollow Frustum/4*(Long Outer Side of Hollow Frustum+Short Outer Side of Hollow Frustum)*sqrt(((cot(pi/Number of Base Vertices of Hollow Frustum))^2*(Long Outer Side of Hollow Frustum-Short Outer Side of Hollow Frustum)^2)+(4*Height of Hollow Frustum^2)))+(Number of Base Vertices of Hollow Frustum/4*(Long Inner Side of Hollow Frustum+Short Inner Side of Hollow Frustum)*sqrt(((cot(pi/Number of Base Vertices of Hollow Frustum))^2*(Long Inner Side of Hollow Frustum-Short Inner Side of Hollow Frustum)^2)+(4*Height of Hollow Frustum^2)))+((Number of Base Vertices of Hollow Frustum*(Long Outer Side of Hollow Frustum^2-Long Inner Side of Hollow Frustum^2))/(4*tan(pi/Number of Base Vertices of Hollow Frustum)))+((Number of Base Vertices of Hollow Frustum*(Short Outer Side of Hollow Frustum^2-Short Inner Side of Hollow Frustum^2))/(4*tan(pi/Number of Base Vertices of Hollow Frustum)))

Total Surface Area of Hollow Frustum Formula

LaTeX Go

What is a Hollow Frustum?

The Hollow Frustum is defined as a Frustum, which is empty from inside and has some difference between the internal (cut-off portion) and external surface. The bottom of the hollow frustum looks like an annular polygon. In other words, the bottom of the hollow cylinder resembles the closed region between two concentric polygons, called the outer and inner polygons with N-sides.

What is Frustum?

In geometry, a Frustum is the portion of a solid that lies between one or two parallel planes cutting it. A right frustum is a parallel truncation of a right pyramid or right cone. In computer graphics, the viewing frustum is the three-dimensional region which is visible on the screen.

How to Calculate Total Surface Area of Hollow Frustum?

Total Surface Area of Hollow Frustum calculator uses Total Surface Area of Hollow Frustum = (Number of Base Vertices of Hollow Frustum/4*(Long Outer Side of Hollow Frustum+Short Outer Side of Hollow Frustum)*sqrt(((cot(pi/Number of Base Vertices of Hollow Frustum))^2*(Long Outer Side of Hollow Frustum-Short Outer Side of Hollow Frustum)^2)+(4*Height of Hollow Frustum^2)))+(Number of Base Vertices of Hollow Frustum/4*(Long Inner Side of Hollow Frustum+Short Inner Side of Hollow Frustum)*sqrt(((cot(pi/Number of Base Vertices of Hollow Frustum))^2*(Long Inner Side of Hollow Frustum-Short Inner Side of Hollow Frustum)^2)+(4*Height of Hollow Frustum^2)))+((Number of Base Vertices of Hollow Frustum*(Long Outer Side of Hollow Frustum^2-Long Inner Side of Hollow Frustum^2))/(4*tan(pi/Number of Base Vertices of Hollow Frustum)))+((Number of Base Vertices of Hollow Frustum*(Short Outer Side of Hollow Frustum^2-Short Inner Side of Hollow Frustum^2))/(4*tan(pi/Number of Base Vertices of Hollow Frustum))) to calculate the Total Surface Area of Hollow Frustum, Total Surface Area of Hollow Frustum formula is defined as the total quantity of plane occupied by the surface of the entire Hollow Frustum. Total Surface Area of Hollow Frustum is denoted by TSA symbol.

How to calculate Total Surface Area of Hollow Frustum using this online calculator? To use this online calculator for Total Surface Area of Hollow Frustum, enter Number of Base Vertices of Hollow Frustum (n), Long Outer Side of Hollow Frustum (S_{Long Outer}), Short Outer Side of Hollow Frustum (S_{Short Outer}), Height of Hollow Frustum (h), Long Inner Side of Hollow Frustum (S_{Long Inner}) & Short Inner Side of Hollow Frustum (S_{Short Inner}) and hit the calculate button. Here is how the Total Surface Area of Hollow Frustum calculation can be explained with given input values -> 646 = (4/4*(14+9)*sqrt(((cot(pi/4))^2*(14-9)^2)+(4*6^2)))+(4/4*(10+5)*sqrt(((cot(pi/4))^2*(10-5)^2)+(4*6^2)))+((4*(14^2-10^2))/(4*tan(pi/4)))+((4*(9^2-5^2))/(4*tan(pi/4))).

FAQ

What is Total Surface Area of Hollow Frustum?

Total Surface Area of Hollow Frustum formula is defined as the total quantity of plane occupied by the surface of the entire Hollow Frustum and is represented as TSA = (n/4*(S_{Long Outer}+S_{Short Outer})*sqrt(((cot(pi/n))^2*(S_{Long Outer}-S_{Short Outer})^2)+(4*h^2)))+(n/4*(S_{Long Inner}+S_{Short Inner})*sqrt(((cot(pi/n))^2*(S_{Long Inner}-S_{Short Inner})^2)+(4*h^2)))+((n*(S_{Long Outer}^2-S_{Long Inner}^2))/(4*tan(pi/n)))+((n*(S_{Short Outer}^2-S_{Short Inner}^2))/(4*tan(pi/n))) or Total Surface Area of Hollow Frustum = (Number of Base Vertices of Hollow Frustum/4*(Long Outer Side of Hollow Frustum+Short Outer Side of Hollow Frustum)*sqrt(((cot(pi/Number of Base Vertices of Hollow Frustum))^2*(Long Outer Side of Hollow Frustum-Short Outer Side of Hollow Frustum)^2)+(4*Height of Hollow Frustum^2)))+(Number of Base Vertices of Hollow Frustum/4*(Long Inner Side of Hollow Frustum+Short Inner Side of Hollow Frustum)*sqrt(((cot(pi/Number of Base Vertices of Hollow Frustum))^2*(Long Inner Side of Hollow Frustum-Short Inner Side of Hollow Frustum)^2)+(4*Height of Hollow Frustum^2)))+((Number of Base Vertices of Hollow Frustum*(Long Outer Side of Hollow Frustum^2-Long Inner Side of Hollow Frustum^2))/(4*tan(pi/Number of Base Vertices of Hollow Frustum)))+((Number of Base Vertices of Hollow Frustum*(Short Outer Side of Hollow Frustum^2-Short Inner Side of Hollow Frustum^2))/(4*tan(pi/Number of Base Vertices of Hollow Frustum))). Number of Base Vertices of Hollow Frustum is the number of vertices of the base polygon of the Hollow Frustum, Long Outer Side of Hollow Frustum is the side length of the outer regular polygon on the base of the Hollow Frustum, Short Outer Side of Hollow Frustum is the side length of the outer regular polygon on the top of the Hollow Frustum, Height of Hollow Frustum is the maximum vertical distance from the bottom to top of the Hollow Frustum, Long Inner Side of Hollow Frustum is the side length of the inner regular polygon on the base of the Hollow Frustum & Short Inner Side of Hollow Frustum is the side length of the inner regular polygon on the top of the Hollow Frustum.

How to calculate Total Surface Area of Hollow Frustum?

Total Surface Area of Hollow Frustum formula is defined as the total quantity of plane occupied by the surface of the entire Hollow Frustum is calculated using Total Surface Area of Hollow Frustum = (Number of Base Vertices of Hollow Frustum/4*(Long Outer Side of Hollow Frustum+Short Outer Side of Hollow Frustum)*sqrt(((cot(pi/Number of Base Vertices of Hollow Frustum))^2*(Long Outer Side of Hollow Frustum-Short Outer Side of Hollow Frustum)^2)+(4*Height of Hollow Frustum^2)))+(Number of Base Vertices of Hollow Frustum/4*(Long Inner Side of Hollow Frustum+Short Inner Side of Hollow Frustum)*sqrt(((cot(pi/Number of Base Vertices of Hollow Frustum))^2*(Long Inner Side of Hollow Frustum-Short Inner Side of Hollow Frustum)^2)+(4*Height of Hollow Frustum^2)))+((Number of Base Vertices of Hollow Frustum*(Long Outer Side of Hollow Frustum^2-Long Inner Side of Hollow Frustum^2))/(4*tan(pi/Number of Base Vertices of Hollow Frustum)))+((Number of Base Vertices of Hollow Frustum*(Short Outer Side of Hollow Frustum^2-Short Inner Side of Hollow Frustum^2))/(4*tan(pi/Number of Base Vertices of Hollow Frustum))). To calculate Total Surface Area of Hollow Frustum, you need Number of Base Vertices of Hollow Frustum (n), Long Outer Side of Hollow Frustum (S_{Long Outer}), Short Outer Side of Hollow Frustum (S_{Short Outer}), Height of Hollow Frustum (h), Long Inner Side of Hollow Frustum (S_{Long Inner}) & Short Inner Side of Hollow Frustum (S_{Short Inner}). With our tool, you need to enter the respective value for Number of Base Vertices of Hollow Frustum, Long Outer Side of Hollow Frustum, Short Outer Side of Hollow Frustum, Height of Hollow Frustum, Long Inner Side of Hollow Frustum & Short Inner Side of Hollow Frustum and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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