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Total Surface Area of Hollow Pyramid given Inner Height and Total Height Formula

GoTotal Surface Area of Hollow Pyramid Formula

GoTotal Surface Area of Hollow Pyramid given Inner Height and Missing Height Formula

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Total Surface Area of Hollow Pyramid is the total amount of two-dimensional space occupied by all the faces of the Hollow Pyramid. Check FAQs

TSA = 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})})

TSA - Total Surface Area 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?

Total Surface Area of Hollow Pyramid given Inner Height and Total Height Example

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

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

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

488.2743 = 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})})

488.2743m² = 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})})

488.2743 = 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})})

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Total Surface Area of Hollow Pyramid given Inner Height and Total Height Solution

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

FIRST Step Consider the formula

TSA = 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})})

Next Step Substitute values of Variables

∴

TSA = 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})})

Next Step Substitute values of Constants

∴

TSA = 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})})

Next Step Prepare to Evaluate

∴

TSA = 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})})

Next Step Evaluate

∴

TSA = 488.27427135769m²

LAST Step Rounding Answer

∴

TSA = 488.2743m²

Total Surface Area of Hollow Pyramid given Inner Height and Total Height Formula Elements

Variables

Constants

Functions

Total Surface Area of Hollow Pyramid

Total Surface Area of Hollow Pyramid is the total amount of two-dimensional space occupied by all the faces of the Hollow Pyramid.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area 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

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 Total Surface Area of Hollow Pyramid

Go Total Surface Area of Hollow Pyramid

TSA = 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})})

Go Total Surface Area of Hollow Pyramid given Inner Height and Missing Height

TSA = 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})})

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

Total Surface Area of Hollow Pyramid given Inner Height and Total Height evaluator uses Total Surface Area 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))) to evaluate the Total Surface Area of Hollow Pyramid, Total Surface Area of Hollow Pyramid given Inner Height and Total Height formula is defined as the total amount of two-dimensional space occupied by all the faces of the Hollow Pyramid and is calculated using the inner height and total height of the Hollow Pyramid. Total Surface Area of Hollow Pyramid is denoted by TSA symbol.

How to evaluate Total Surface Area of Hollow Pyramid given Inner Height and Total Height using this online evaluator? To use this online evaluator for Total Surface Area of Hollow Pyramid given Inner Height and Total 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 Total Surface Area of Hollow Pyramid given Inner Height and Total Height

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

The formula of Total Surface Area of Hollow Pyramid given Inner Height and Total Height is expressed as Total Surface Area 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))). Here is an example- 488.2743 = 4*10/2*(sqrt(15^2+(10^2/4*(cot(pi/4))^2))+sqrt((15-8)^2+(10^2/4*(cot(pi/4))^2))).

How to calculate Total Surface Area of Hollow Pyramid given Inner Height and Total 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 Total Surface Area of Hollow Pyramid given Inner Height and Total Height using the formula - Total Surface Area 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))). This formula also uses Archimedes' constant and , Cotangent (cot), Square Root (sqrt) function(s).

What are the other ways to Calculate Total Surface Area of Hollow Pyramid?

Here are the different ways to Calculate Total Surface Area of Hollow Pyramid-

Total Surface Area 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)))
Total Surface Area 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)))

Can the Total Surface Area of Hollow Pyramid given Inner Height and Total Height be negative?

No, the Total Surface Area of Hollow Pyramid given Inner Height and Total Height, measured in Area cannot be negative.

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

Total Surface Area of Hollow Pyramid given Inner Height and Total Height 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 Pyramid given Inner Height and Total Height can be measured.

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Total Surface Area of Hollow Pyramid given Inner Height and Total Height Formula

​GoTotal Surface Area of Hollow Pyramid Formula

​GoTotal Surface Area of Hollow Pyramid given Inner Height and Missing Height Formula

Total Surface Area of Hollow Pyramid given Inner Height and Total Height Example

Total Surface Area of Hollow Pyramid given Inner Height and Total Height Solution

Total Surface Area of Hollow Pyramid given Inner Height and Total Height Formula Elements

Other Formulas to find Total Surface Area of Hollow Pyramid

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

FAQs on Total Surface Area of Hollow Pyramid given Inner Height and Total Height

Variable Name

GoTotal Surface Area of Hollow Pyramid Formula

GoTotal Surface Area of Hollow Pyramid given Inner Height and Missing Height Formula