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Total Surface Area of Hollow Frustum Formula

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Total Surface Area of Hollow Frustum is the total quantity of plane occupied by the surface of the entire Hollow Frustum. Check FAQs

TSA = (\frac{n}{4} \cdot (S Long Outer + S Short Outer) \cdot \sqrt{({(\cot (\frac{π}{n}))}^{2} \cdot {(S Long Outer - S Short Outer)}^{2}) + (4 \cdot h^{2})}) + (\frac{n}{4} \cdot (S Long Inner + S Short Inner) \cdot \sqrt{({(\cot (\frac{π}{n}))}^{2} \cdot {(S Long Inner - S Short Inner)}^{2}) + (4 \cdot h^{2})}) + (\frac{n \cdot ({S Long Outer}^{2} - {S Long Inner}^{2})}{4 \cdot \tan (\frac{π}{n})}) + (\frac{n \cdot ({S Short Outer}^{2} - {S Short Inner}^{2})}{4 \cdot \tan (\frac{π}{n})})

TSA - Total Surface Area of Hollow Frustum?n - Number of Base Vertices of Hollow Frustum?S_{Long Outer} - Long Outer Side of Hollow Frustum?S_{Short Outer} - Short Outer Side of Hollow Frustum?h - Height of Hollow Frustum?S_{Long Inner} - Long Inner Side of Hollow Frustum?S_{Short Inner} - Short Inner Side of Hollow Frustum?π - Archimedes' constant?

Total Surface Area of Hollow Frustum Example

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Here is how the Total Surface Area of Hollow Frustum equation looks like with Values.

Here is how the Total Surface Area of Hollow Frustum equation looks like with Units.

Here is how the Total Surface Area of Hollow Frustum equation looks like.

646 = (\frac{4}{4} \cdot (14 + 9) \cdot \sqrt{({(\cot (\frac{3.1416}{4}))}^{2} \cdot {(14 - 9)}^{2}) + (4 \cdot 6^{2})}) + (\frac{4}{4} \cdot (10 + 5) \cdot \sqrt{({(\cot (\frac{3.1416}{4}))}^{2} \cdot {(10 - 5)}^{2}) + (4 \cdot 6^{2})}) + (\frac{4 \cdot (14^{2} - 10^{2})}{4 \cdot \tan (\frac{3.1416}{4})}) + (\frac{4 \cdot (9^{2} - 5^{2})}{4 \cdot \tan (\frac{3.1416}{4})})

646m² = (\frac{4}{4} \cdot (14m + 9m) \cdot \sqrt{({(\cot (\frac{3.1416}{4}))}^{2} \cdot {(14m - 9m)}^{2}) + (4 \cdot {6m}^{2})}) + (\frac{4}{4} \cdot (10m + 5m) \cdot \sqrt{({(\cot (\frac{3.1416}{4}))}^{2} \cdot {(10m - 5m)}^{2}) + (4 \cdot {6m}^{2})}) + (\frac{4 \cdot ({14m}^{2} - {10m}^{2})}{4 \cdot \tan (\frac{3.1416}{4})}) + (\frac{4 \cdot ({9m}^{2} - {5m}^{2})}{4 \cdot \tan (\frac{3.1416}{4})})

646 = (\frac{4}{4} \cdot (14 + 9) \cdot \sqrt{({(\cot (\frac{3.1416}{4}))}^{2} \cdot {(14 - 9)}^{2}) + (4 \cdot 6^{2})}) + (\frac{4}{4} \cdot (10 + 5) \cdot \sqrt{({(\cot (\frac{3.1416}{4}))}^{2} \cdot {(10 - 5)}^{2}) + (4 \cdot 6^{2})}) + (\frac{4 \cdot (14^{2} - 10^{2})}{4 \cdot \tan (\frac{3.1416}{4})}) + (\frac{4 \cdot (9^{2} - 5^{2})}{4 \cdot \tan (\frac{3.1416}{4})})

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Total Surface Area of Hollow Frustum Solution

Follow our step by step solution on how to calculate Total Surface Area of Hollow Frustum?

FIRST Step Consider the formula

TSA = (\frac{n}{4} \cdot (S Long Outer + S Short Outer) \cdot \sqrt{({(\cot (\frac{π}{n}))}^{2} \cdot {(S Long Outer - S Short Outer)}^{2}) + (4 \cdot h^{2})}) + (\frac{n}{4} \cdot (S Long Inner + S Short Inner) \cdot \sqrt{({(\cot (\frac{π}{n}))}^{2} \cdot {(S Long Inner - S Short Inner)}^{2}) + (4 \cdot h^{2})}) + (\frac{n \cdot ({S Long Outer}^{2} - {S Long Inner}^{2})}{4 \cdot \tan (\frac{π}{n})}) + (\frac{n \cdot ({S Short Outer}^{2} - {S Short Inner}^{2})}{4 \cdot \tan (\frac{π}{n})})

Next Step Substitute values of Variables

∴

TSA = (\frac{4}{4} \cdot (14m + 9m) \cdot \sqrt{({(\cot (\frac{π}{4}))}^{2} \cdot {(14m - 9m)}^{2}) + (4 \cdot {6m}^{2})}) + (\frac{4}{4} \cdot (10m + 5m) \cdot \sqrt{({(\cot (\frac{π}{4}))}^{2} \cdot {(10m - 5m)}^{2}) + (4 \cdot {6m}^{2})}) + (\frac{4 \cdot ({14m}^{2} - {10m}^{2})}{4 \cdot \tan (\frac{π}{4})}) + (\frac{4 \cdot ({9m}^{2} - {5m}^{2})}{4 \cdot \tan (\frac{π}{4})})

Next Step Substitute values of Constants

∴

TSA = (\frac{4}{4} \cdot (14m + 9m) \cdot \sqrt{({(\cot (\frac{3.1416}{4}))}^{2} \cdot {(14m - 9m)}^{2}) + (4 \cdot {6m}^{2})}) + (\frac{4}{4} \cdot (10m + 5m) \cdot \sqrt{({(\cot (\frac{3.1416}{4}))}^{2} \cdot {(10m - 5m)}^{2}) + (4 \cdot {6m}^{2})}) + (\frac{4 \cdot ({14m}^{2} - {10m}^{2})}{4 \cdot \tan (\frac{3.1416}{4})}) + (\frac{4 \cdot ({9m}^{2} - {5m}^{2})}{4 \cdot \tan (\frac{3.1416}{4})})

Next Step Prepare to Evaluate

∴

TSA = (\frac{4}{4} \cdot (14 + 9) \cdot \sqrt{({(\cot (\frac{3.1416}{4}))}^{2} \cdot {(14 - 9)}^{2}) + (4 \cdot 6^{2})}) + (\frac{4}{4} \cdot (10 + 5) \cdot \sqrt{({(\cot (\frac{3.1416}{4}))}^{2} \cdot {(10 - 5)}^{2}) + (4 \cdot 6^{2})}) + (\frac{4 \cdot (14^{2} - 10^{2})}{4 \cdot \tan (\frac{3.1416}{4})}) + (\frac{4 \cdot (9^{2} - 5^{2})}{4 \cdot \tan (\frac{3.1416}{4})})

LAST Step Evaluate

∴

TSA = 646m²

Total Surface Area of Hollow Frustum Formula Elements

Variables

Constants

Functions

Total Surface Area of Hollow Frustum

Total Surface Area of Hollow Frustum is the total quantity of plane occupied by the surface of the entire Hollow Frustum.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of 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.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Base Vertices of Hollow Frustum

Long Outer Side of Hollow Frustum

Long Outer Side of Hollow Frustum is the side length of the outer regular polygon on the base of the Hollow Frustum.

Symbol: S_{Long Outer}

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Long Outer Side of Hollow Frustum

Short Outer Side of Hollow Frustum

Short Outer Side of Hollow Frustum is the side length of the outer regular polygon on the top of the Hollow Frustum.

Symbol: S_{Short Outer}

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Short Outer Side of Hollow Frustum

Height of Hollow Frustum

Height of Hollow Frustum is the maximum vertical distance from the bottom to top of the Hollow Frustum.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Hollow Frustum

Long Inner Side of Hollow Frustum

Long Inner Side of Hollow Frustum is the side length of the inner regular polygon on the base of the Hollow Frustum.

Symbol: S_{Long Inner}

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Long Inner Side of Hollow Frustum

Short Inner Side of Hollow Frustum

Short Inner Side of Hollow Frustum is the side length of the inner regular polygon on the top of the Hollow Frustum.

Symbol: S_{Short Inner}

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Short Inner Side of Hollow Frustum

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: 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.

Syntax: 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.

Syntax: sqrt(Number)

How to Evaluate Total Surface Area of Hollow Frustum?

Total Surface Area of Hollow Frustum evaluator 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 evaluate 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 evaluate Total Surface Area of Hollow Frustum using this online evaluator? To use this online evaluator 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.

FAQs on Total Surface Area of Hollow Frustum

What is the formula to find Total Surface Area of Hollow Frustum?

The formula of Total Surface Area of Hollow Frustum is expressed as 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))). Here is an example- 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))).

How to calculate Total Surface Area of Hollow Frustum?

With 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}) we can find Total Surface Area of Hollow Frustum using the formula - 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))). This formula also uses Archimedes' constant and , Tangent (tan), Cotangent (cot), Square Root (sqrt) function(s).

Can the Total Surface Area of Hollow Frustum be negative?

No, the Total Surface Area of Hollow Frustum, measured in Area cannot be negative.

Which unit is used to measure Total Surface Area of Hollow Frustum?

Total Surface Area of Hollow Frustum is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Total Surface Area of Hollow Frustum can be measured.

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Total Surface Area of Hollow Frustum Formula

Total Surface Area of Hollow Frustum Example

Total Surface Area of Hollow Frustum Solution

Total Surface Area of Hollow Frustum Formula Elements

How to Evaluate Total Surface Area of Hollow Frustum?

FAQs on Total Surface Area of Hollow Frustum

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