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Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height Formula

GoSurface to Volume Ratio of Hollow Pyramid Formula

GoSurface to Volume Ratio of Hollow Pyramid given Inner Height and Missing Height Formula

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Surface to Volume Ratio of Hollow Pyramid is the numerical ratio of the total surface area of the Hollow Pyramid to the volume of the Hollow Pyramid. Check FAQs

R A/V = \frac{n \cdot \frac{l e(Base)}{2} \cdot (\sqrt{{h Total}^{2} + (\frac{{l e(Base)}^{2}}{4} \cdot {(\cot (\frac{π}{n}))}^{2})} + \sqrt{{(h Total - h Inner)}^{2} + (\frac{{l e(Base)}^{2}}{4} \cdot {(\cot (\frac{π}{n}))}^{2})})}{\frac{\frac{1}{3} \cdot n \cdot h Inner \cdot {l e(Base)}^{2}}{4 \cdot \tan (\frac{π}{n})}}

R_A/V - Surface to Volume Ratio of Hollow Pyramid?n - Number of Base Vertices of Hollow Pyramid?l_e(Base) - Edge Length of Base of Hollow Pyramid?h_Total - Total Height of Hollow Pyramid?h_Inner - Inner Height of Hollow Pyramid?π - Archimedes' constant?

Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height Example

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Here is how the Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height equation looks like with Values.

Here is how the Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height equation looks like with Units.

Here is how the Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height equation looks like.

1.831 = \frac{4 \cdot \frac{10}{2} \cdot (\sqrt{15^{2} + (\frac{10^{2}}{4} \cdot {(\cot (\frac{3.1416}{4}))}^{2})} + \sqrt{{(15 - 8)}^{2} + (\frac{10^{2}}{4} \cdot {(\cot (\frac{3.1416}{4}))}^{2})})}{\frac{\frac{1}{3} \cdot 4 \cdot 8 \cdot 10^{2}}{4 \cdot \tan (\frac{3.1416}{4})}}

1.831m⁻¹ = \frac{4 \cdot \frac{10m}{2} \cdot (\sqrt{{15m}^{2} + (\frac{{10m}^{2}}{4} \cdot {(\cot (\frac{3.1416}{4}))}^{2})} + \sqrt{{(15m - 8m)}^{2} + (\frac{{10m}^{2}}{4} \cdot {(\cot (\frac{3.1416}{4}))}^{2})})}{\frac{\frac{1}{3} \cdot 4 \cdot 8m \cdot {10m}^{2}}{4 \cdot \tan (\frac{3.1416}{4})}}

1.831 = \frac{4 \cdot \frac{10}{2} \cdot (\sqrt{15^{2} + (\frac{10^{2}}{4} \cdot {(\cot (\frac{3.1416}{4}))}^{2})} + \sqrt{{(15 - 8)}^{2} + (\frac{10^{2}}{4} \cdot {(\cot (\frac{3.1416}{4}))}^{2})})}{\frac{\frac{1}{3} \cdot 4 \cdot 8 \cdot 10^{2}}{4 \cdot \tan (\frac{3.1416}{4})}}

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Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height Solution

Follow our step by step solution on how to calculate Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height?

FIRST Step Consider the formula

R A/V = \frac{n \cdot \frac{l e(Base)}{2} \cdot (\sqrt{{h Total}^{2} + (\frac{{l e(Base)}^{2}}{4} \cdot {(\cot (\frac{π}{n}))}^{2})} + \sqrt{{(h Total - h Inner)}^{2} + (\frac{{l e(Base)}^{2}}{4} \cdot {(\cot (\frac{π}{n}))}^{2})})}{\frac{\frac{1}{3} \cdot n \cdot h Inner \cdot {l e(Base)}^{2}}{4 \cdot \tan (\frac{π}{n})}}

Next Step Substitute values of Variables

∴

R A/V = \frac{4 \cdot \frac{10m}{2} \cdot (\sqrt{{15m}^{2} + (\frac{{10m}^{2}}{4} \cdot {(\cot (\frac{π}{4}))}^{2})} + \sqrt{{(15m - 8m)}^{2} + (\frac{{10m}^{2}}{4} \cdot {(\cot (\frac{π}{4}))}^{2})})}{\frac{\frac{1}{3} \cdot 4 \cdot 8m \cdot {10m}^{2}}{4 \cdot \tan (\frac{π}{4})}}

Next Step Substitute values of Constants

∴

R A/V = \frac{4 \cdot \frac{10m}{2} \cdot (\sqrt{{15m}^{2} + (\frac{{10m}^{2}}{4} \cdot {(\cot (\frac{3.1416}{4}))}^{2})} + \sqrt{{(15m - 8m)}^{2} + (\frac{{10m}^{2}}{4} \cdot {(\cot (\frac{3.1416}{4}))}^{2})})}{\frac{\frac{1}{3} \cdot 4 \cdot 8m \cdot {10m}^{2}}{4 \cdot \tan (\frac{3.1416}{4})}}

Next Step Prepare to Evaluate

∴

R A/V = \frac{4 \cdot \frac{10}{2} \cdot (\sqrt{15^{2} + (\frac{10^{2}}{4} \cdot {(\cot (\frac{3.1416}{4}))}^{2})} + \sqrt{{(15 - 8)}^{2} + (\frac{10^{2}}{4} \cdot {(\cot (\frac{3.1416}{4}))}^{2})})}{\frac{\frac{1}{3} \cdot 4 \cdot 8 \cdot 10^{2}}{4 \cdot \tan (\frac{3.1416}{4})}}

Next Step Evaluate

∴

R A/V = 1.83102851759134m⁻¹

LAST Step Rounding Answer

∴

R A/V = 1.831m⁻¹

Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height Formula Elements

Variables

Constants

Functions

Surface to Volume Ratio of Hollow Pyramid

Surface to Volume Ratio of Hollow Pyramid is the numerical ratio of the total surface area of the Hollow Pyramid to the volume of the Hollow Pyramid.

Symbol: R_A/V

Measurement: Reciprocal LengthUnit: m⁻¹

Note: Value should be greater than 0.

Formulas to find Surface to Volume Ratio of Hollow Pyramid

Number of Base Vertices of Hollow Pyramid

Number of Base Vertices of Hollow Pyramid are the number of base vertices of a regular Hollow Pyramid.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Base Vertices of Hollow Pyramid

Edge Length of Base of Hollow Pyramid

Edge Length of Base of Hollow Pyramid is the length of the straight line connecting any two adjacent vertices on the base of the Hollow Pyramid.

Symbol: l_e(Base)

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length of Base of Hollow Pyramid

Total Height of Hollow Pyramid

Total Height of Hollow Pyramid is the total length of the perpendicular from the apex to the base of the complete pyramid in the Hollow Pyramid.

Symbol: h_Total

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Total Height of Hollow Pyramid

Inner Height of Hollow Pyramid

Inner Height of Hollow Pyramid is the length of the perpendicular from the apex of the complete pyramid to the apex of the removed pyramid in the Hollow Pyramid.

Symbol: h_Inner

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inner Height of Hollow Pyramid

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)

Other Formulas to find Surface to Volume Ratio of Hollow Pyramid

Go Surface to Volume Ratio of Hollow Pyramid

R A/V = \frac{n \cdot \frac{l e(Base)}{2} \cdot (\sqrt{{h Total}^{2} + (\frac{{l e(Base)}^{2}}{4} \cdot {(\cot (\frac{π}{n}))}^{2})} + \sqrt{{h Missing}^{2} + (\frac{{l e(Base)}^{2}}{4} \cdot {(\cot (\frac{π}{n}))}^{2})})}{\frac{\frac{1}{3} \cdot n \cdot (h Total - h Missing) \cdot {l e(Base)}^{2}}{4 \cdot \tan (\frac{π}{n})}}

Go Surface to Volume Ratio of Hollow Pyramid given Inner Height and Missing Height

R A/V = \frac{n \cdot \frac{l e(Base)}{2} \cdot (\sqrt{{(h Inner + h Missing)}^{2} + (\frac{{l e(Base)}^{2}}{4} \cdot {(\cot (\frac{π}{n}))}^{2})} + \sqrt{{h Missing}^{2} + (\frac{{l e(Base)}^{2}}{4} \cdot {(\cot (\frac{π}{n}))}^{2})})}{\frac{\frac{1}{3} \cdot n \cdot h Inner \cdot {l e(Base)}^{2}}{4 \cdot \tan (\frac{π}{n})}}

How to Evaluate Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height?

Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height evaluator uses Surface to Volume Ratio of Hollow Pyramid = (Number of Base Vertices of Hollow Pyramid*Edge Length of Base of Hollow Pyramid/2*(sqrt(Total Height of Hollow Pyramid^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2))+sqrt((Total Height of Hollow Pyramid-Inner Height of Hollow Pyramid)^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2))))/((1/3*Number of Base Vertices of Hollow Pyramid*Inner Height of Hollow Pyramid*Edge Length of Base of Hollow Pyramid^2)/(4*tan(pi/Number of Base Vertices of Hollow Pyramid))) to evaluate the Surface to Volume Ratio of Hollow Pyramid, Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height formula is defined as the numerical ratio of the total surface area of the Hollow Pyramid to the volume of the Hollow Pyramid and is calculated using the inner height and total height of the Hollow Pyramid. Surface to Volume Ratio of Hollow Pyramid is denoted by R_A/V symbol.

How to evaluate Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height using this online evaluator? To use this online evaluator for Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height, enter Number of Base Vertices of Hollow Pyramid (n), Edge Length of Base of Hollow Pyramid (l_e(Base)), Total Height of Hollow Pyramid (h_Total) & Inner Height of Hollow Pyramid (h_Inner) and hit the calculate button.

FAQs on Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height

What is the formula to find Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height?

The formula of Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height is expressed as Surface to Volume Ratio of Hollow Pyramid = (Number of Base Vertices of Hollow Pyramid*Edge Length of Base of Hollow Pyramid/2*(sqrt(Total Height of Hollow Pyramid^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2))+sqrt((Total Height of Hollow Pyramid-Inner Height of Hollow Pyramid)^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2))))/((1/3*Number of Base Vertices of Hollow Pyramid*Inner Height of Hollow Pyramid*Edge Length of Base of Hollow Pyramid^2)/(4*tan(pi/Number of Base Vertices of Hollow Pyramid))). Here is an example- 1.831029 = (4*10/2*(sqrt(15^2+(10^2/4*(cot(pi/4))^2))+sqrt((15-8)^2+(10^2/4*(cot(pi/4))^2))))/((1/3*4*8*10^2)/(4*tan(pi/4))).

How to calculate Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height?

With Number of Base Vertices of Hollow Pyramid (n), Edge Length of Base of Hollow Pyramid (l_e(Base)), Total Height of Hollow Pyramid (h_Total) & Inner Height of Hollow Pyramid (h_Inner) we can find Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height using the formula - Surface to Volume Ratio of Hollow Pyramid = (Number of Base Vertices of Hollow Pyramid*Edge Length of Base of Hollow Pyramid/2*(sqrt(Total Height of Hollow Pyramid^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2))+sqrt((Total Height of Hollow Pyramid-Inner Height of Hollow Pyramid)^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2))))/((1/3*Number of Base Vertices of Hollow Pyramid*Inner Height of Hollow Pyramid*Edge Length of Base of Hollow Pyramid^2)/(4*tan(pi/Number of Base Vertices of Hollow Pyramid))). This formula also uses Archimedes' constant and , Tangent (tan), Cotangent (cot), Square Root (sqrt) function(s).

What are the other ways to Calculate Surface to Volume Ratio of Hollow Pyramid?

Here are the different ways to Calculate Surface to Volume Ratio of Hollow Pyramid-

Surface to Volume Ratio of Hollow Pyramid=(Number of Base Vertices of Hollow Pyramid*Edge Length of Base of Hollow Pyramid/2*(sqrt(Total Height of Hollow Pyramid^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2))+sqrt(Missing Height of Hollow Pyramid^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2))))/((1/3*Number of Base Vertices of Hollow Pyramid*(Total Height of Hollow Pyramid-Missing Height of Hollow Pyramid)*Edge Length of Base of Hollow Pyramid^2)/(4*tan(pi/Number of Base Vertices of Hollow Pyramid)))
Surface to Volume Ratio of Hollow Pyramid=(Number of Base Vertices of Hollow Pyramid*Edge Length of Base of Hollow Pyramid/2*(sqrt((Inner Height of Hollow Pyramid+Missing Height of Hollow Pyramid)^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2))+sqrt(Missing Height of Hollow Pyramid^2+(Edge Length of Base of Hollow Pyramid^2/4*(cot(pi/Number of Base Vertices of Hollow Pyramid))^2))))/((1/3*Number of Base Vertices of Hollow Pyramid*Inner Height of Hollow Pyramid*Edge Length of Base of Hollow Pyramid^2)/(4*tan(pi/Number of Base Vertices of Hollow Pyramid)))

Can the Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height be negative?

No, the Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height, measured in Reciprocal Length cannot be negative.

Which unit is used to measure Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height?

Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height is usually measured using the 1 per Meter[m⁻¹] for Reciprocal Length. 1 per Kilometer[m⁻¹], 1 per Mile[m⁻¹], 1 per Yard[m⁻¹] are the few other units in which Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height can be measured.

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Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height Formula

​GoSurface to Volume Ratio of Hollow Pyramid Formula

​GoSurface to Volume Ratio of Hollow Pyramid given Inner Height and Missing Height Formula

Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height Example

Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height Solution

Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height Formula Elements

Other Formulas to find Surface to Volume Ratio of Hollow Pyramid

How to Evaluate Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height?

FAQs on Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height

Variable Name

GoSurface to Volume Ratio of Hollow Pyramid Formula

GoSurface to Volume Ratio of Hollow Pyramid given Inner Height and Missing Height Formula