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Volume of Hollow Frustum Formula

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Volume of Hollow Frustum is the total quantity of space enclosed by the surface of the entire Hollow Frustum. Check FAQs

V = \frac{h}{3} \cdot ((\frac{n \cdot ({S Long Outer}^{2} + {S Short Outer}^{2})}{4 \cdot \tan (\frac{π}{n})}) + (\frac{n \cdot S Long Outer \cdot S Short Outer}{4 \cdot \tan (\frac{π}{n})}) - (\frac{n \cdot ({S Long Inner}^{2} + {S Short Inner}^{2})}{4 \cdot \tan (\frac{π}{n})}) - (\frac{n \cdot S Long Inner \cdot S Short Inner}{4 \cdot \tan (\frac{π}{n})}))

V - Volume of Hollow Frustum?h - Height 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?S_{Long Inner} - Long Inner Side of Hollow Frustum?S_{Short Inner} - Short Inner Side of Hollow Frustum?π - Archimedes' constant?

Volume of Hollow Frustum Example

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Here is how the Volume of Hollow Frustum equation looks like with Values.

Here is how the Volume of Hollow Frustum equation looks like with Units.

Here is how the Volume of Hollow Frustum equation looks like.

456 = \frac{6}{3} \cdot ((\frac{4 \cdot (14^{2} + 9^{2})}{4 \cdot \tan (\frac{3.1416}{4})}) + (\frac{4 \cdot 14 \cdot 9}{4 \cdot \tan (\frac{3.1416}{4})}) - (\frac{4 \cdot (10^{2} + 5^{2})}{4 \cdot \tan (\frac{3.1416}{4})}) - (\frac{4 \cdot 10 \cdot 5}{4 \cdot \tan (\frac{3.1416}{4})}))

456m³ = \frac{6m}{3} \cdot ((\frac{4 \cdot ({14m}^{2} + {9m}^{2})}{4 \cdot \tan (\frac{3.1416}{4})}) + (\frac{4 \cdot 14m \cdot 9m}{4 \cdot \tan (\frac{3.1416}{4})}) - (\frac{4 \cdot ({10m}^{2} + {5m}^{2})}{4 \cdot \tan (\frac{3.1416}{4})}) - (\frac{4 \cdot 10m \cdot 5m}{4 \cdot \tan (\frac{3.1416}{4})}))

456 = \frac{6}{3} \cdot ((\frac{4 \cdot (14^{2} + 9^{2})}{4 \cdot \tan (\frac{3.1416}{4})}) + (\frac{4 \cdot 14 \cdot 9}{4 \cdot \tan (\frac{3.1416}{4})}) - (\frac{4 \cdot (10^{2} + 5^{2})}{4 \cdot \tan (\frac{3.1416}{4})}) - (\frac{4 \cdot 10 \cdot 5}{4 \cdot \tan (\frac{3.1416}{4})}))

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Volume of Hollow Frustum Solution

Follow our step by step solution on how to calculate Volume of Hollow Frustum?

FIRST Step Consider the formula

V = \frac{h}{3} \cdot ((\frac{n \cdot ({S Long Outer}^{2} + {S Short Outer}^{2})}{4 \cdot \tan (\frac{π}{n})}) + (\frac{n \cdot S Long Outer \cdot S Short Outer}{4 \cdot \tan (\frac{π}{n})}) - (\frac{n \cdot ({S Long Inner}^{2} + {S Short Inner}^{2})}{4 \cdot \tan (\frac{π}{n})}) - (\frac{n \cdot S Long Inner \cdot S Short Inner}{4 \cdot \tan (\frac{π}{n})}))

Next Step Substitute values of Variables

∴

V = \frac{6m}{3} \cdot ((\frac{4 \cdot ({14m}^{2} + {9m}^{2})}{4 \cdot \tan (\frac{π}{4})}) + (\frac{4 \cdot 14m \cdot 9m}{4 \cdot \tan (\frac{π}{4})}) - (\frac{4 \cdot ({10m}^{2} + {5m}^{2})}{4 \cdot \tan (\frac{π}{4})}) - (\frac{4 \cdot 10m \cdot 5m}{4 \cdot \tan (\frac{π}{4})}))

Next Step Substitute values of Constants

∴

V = \frac{6m}{3} \cdot ((\frac{4 \cdot ({14m}^{2} + {9m}^{2})}{4 \cdot \tan (\frac{3.1416}{4})}) + (\frac{4 \cdot 14m \cdot 9m}{4 \cdot \tan (\frac{3.1416}{4})}) - (\frac{4 \cdot ({10m}^{2} + {5m}^{2})}{4 \cdot \tan (\frac{3.1416}{4})}) - (\frac{4 \cdot 10m \cdot 5m}{4 \cdot \tan (\frac{3.1416}{4})}))

Next Step Prepare to Evaluate

∴

V = \frac{6}{3} \cdot ((\frac{4 \cdot (14^{2} + 9^{2})}{4 \cdot \tan (\frac{3.1416}{4})}) + (\frac{4 \cdot 14 \cdot 9}{4 \cdot \tan (\frac{3.1416}{4})}) - (\frac{4 \cdot (10^{2} + 5^{2})}{4 \cdot \tan (\frac{3.1416}{4})}) - (\frac{4 \cdot 10 \cdot 5}{4 \cdot \tan (\frac{3.1416}{4})}))

LAST Step Evaluate

∴

V = 456m³

Volume of Hollow Frustum Formula Elements

Variables

Constants

Functions

Volume of Hollow Frustum

Volume of Hollow Frustum is the total quantity of space enclosed by the surface of the entire Hollow Frustum.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume 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

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

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)

How to Evaluate Volume of Hollow Frustum?

Volume of Hollow Frustum evaluator uses Volume of Hollow Frustum = Height of Hollow Frustum/3*(((Number of Base Vertices of Hollow Frustum*(Long Outer Side of Hollow Frustum^2+Short Outer Side of Hollow Frustum^2))/(4*tan(pi/Number of Base Vertices of Hollow Frustum)))+((Number of Base Vertices of Hollow Frustum*Long Outer Side of Hollow Frustum*Short Outer Side of Hollow Frustum)/(4*tan(pi/Number of Base Vertices of Hollow Frustum)))-((Number of Base Vertices of Hollow Frustum*(Long Inner 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*Long Inner Side of Hollow Frustum*Short Inner Side of Hollow Frustum)/(4*tan(pi/Number of Base Vertices of Hollow Frustum)))) to evaluate the Volume of Hollow Frustum, Volume of Hollow Frustum formula is defined as the total quantity of space enclosed by the surface of the entire Hollow Frustum. Volume of Hollow Frustum is denoted by V symbol.

How to evaluate Volume of Hollow Frustum using this online evaluator? To use this online evaluator for Volume of Hollow Frustum, enter Height of Hollow Frustum (h), 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}), 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 Volume of Hollow Frustum

What is the formula to find Volume of Hollow Frustum?

The formula of Volume of Hollow Frustum is expressed as Volume of Hollow Frustum = Height of Hollow Frustum/3*(((Number of Base Vertices of Hollow Frustum*(Long Outer Side of Hollow Frustum^2+Short Outer Side of Hollow Frustum^2))/(4*tan(pi/Number of Base Vertices of Hollow Frustum)))+((Number of Base Vertices of Hollow Frustum*Long Outer Side of Hollow Frustum*Short Outer Side of Hollow Frustum)/(4*tan(pi/Number of Base Vertices of Hollow Frustum)))-((Number of Base Vertices of Hollow Frustum*(Long Inner 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*Long Inner Side of Hollow Frustum*Short Inner Side of Hollow Frustum)/(4*tan(pi/Number of Base Vertices of Hollow Frustum)))). Here is an example- 456 = 6/3*(((4*(14^2+9^2))/(4*tan(pi/4)))+((4*14*9)/(4*tan(pi/4)))-((4*(10^2+5^2))/(4*tan(pi/4)))-((4*10*5)/(4*tan(pi/4)))).

How to calculate Volume of Hollow Frustum?

With Height of Hollow Frustum (h), 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}), Long Inner Side of Hollow Frustum (S_{Long Inner}) & Short Inner Side of Hollow Frustum (S_{Short Inner}) we can find Volume of Hollow Frustum using the formula - Volume of Hollow Frustum = Height of Hollow Frustum/3*(((Number of Base Vertices of Hollow Frustum*(Long Outer Side of Hollow Frustum^2+Short Outer Side of Hollow Frustum^2))/(4*tan(pi/Number of Base Vertices of Hollow Frustum)))+((Number of Base Vertices of Hollow Frustum*Long Outer Side of Hollow Frustum*Short Outer Side of Hollow Frustum)/(4*tan(pi/Number of Base Vertices of Hollow Frustum)))-((Number of Base Vertices of Hollow Frustum*(Long Inner 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*Long Inner Side of Hollow Frustum*Short Inner Side of Hollow Frustum)/(4*tan(pi/Number of Base Vertices of Hollow Frustum)))). This formula also uses Archimedes' constant and Tangent (tan) function(s).

Can the Volume of Hollow Frustum be negative?

No, the Volume of Hollow Frustum, measured in Volume cannot be negative.

Which unit is used to measure Volume of Hollow Frustum?

Volume of Hollow Frustum is usually measured using the Cubic Meter[m³] for Volume. Cubic Centimeter[m³], Cubic Millimeter[m³], Liter[m³] are the few other units in which Volume of Hollow Frustum can be measured.

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Volume of Hollow Frustum Formula

Volume of Hollow Frustum Example

Volume of Hollow Frustum Solution

Volume of Hollow Frustum Formula Elements

How to Evaluate Volume of Hollow Frustum?

FAQs on Volume of Hollow Frustum

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