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

✖Number of Base Vertices of Hollow Pyramid are the number of base vertices of a regular Hollow Pyramid.ⓘ Number of Base Vertices of Hollow Pyramid [n]			+10% -10%
✖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.ⓘ Edge Length of Base of Hollow Pyramid [l_e(Base)]			+10% -10%
✖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.ⓘ Total Height of Hollow Pyramid [h_Total]			+10% -10%
✖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.ⓘ Inner Height of Hollow Pyramid [h_Inner]			+10% -10%

✖Total Surface Area of Hollow Pyramid is the total amount of two-dimensional space occupied by all the faces of the Hollow Pyramid.ⓘ Total Surface Area of Hollow Pyramid given Inner Height and Total Height [TSA]

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

STEP 0: Pre-Calculation Summary

Formula Used

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)))
TSA = n*l_e(Base)/2*(sqrt(h_Total^2+(l_e(Base)^2/4*(cot(pi/n))^2))+sqrt((h_Total-h_Inner)^2+(l_e(Base)^2/4*(cot(pi/n))^2)))
This formula uses 1 Constants, 2 Functions, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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 Pyramid - (Measured in Square Meter) - Total Surface Area of Hollow Pyramid is the total amount of two-dimensional space occupied by all the faces of the 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.
Edge Length of Base of Hollow Pyramid - (Measured in Meter) - 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.
Total Height of Hollow Pyramid - (Measured in Meter) - 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.
Inner Height of Hollow Pyramid - (Measured in Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Number of Base Vertices of Hollow Pyramid: 4 --> No Conversion Required
Edge Length of Base of Hollow Pyramid: 10 Meter --> 10 Meter No Conversion Required
Total Height of Hollow Pyramid: 15 Meter --> 15 Meter No Conversion Required
Inner Height of Hollow Pyramid: 8 Meter --> 8 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = n*l_e(Base)/2*(sqrt(h_Total^2+(l_e(Base)^2/4*(cot(pi/n))^2))+sqrt((h_Total-h_Inner)^2+(l_e(Base)^2/4*(cot(pi/n))^2))) --> 4*10/2*(sqrt(15^2+(10^2/4*(cot(pi/4))^2))+sqrt((15-8)^2+(10^2/4*(cot(pi/4))^2)))

Evaluating ... ...

TSA = 488.27427135769

STEP 3: Convert Result to Output's Unit

488.27427135769 Square Meter --> No Conversion Required

FINAL ANSWER

488.27427135769 ≈ 488.2743 Square Meter <-- Total Surface Area of Hollow Pyramid

(Calculation completed in 00.007 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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< Surface Area of Hollow Pyramid Calculators

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

LaTeX Go 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)))

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

LaTeX Go 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)))

Total Surface Area of Hollow Pyramid

LaTeX Go 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 given Inner Height and Total Height Formula

LaTeX Go

What is a Hollow Pyramid?

A Hollow Pyramid is a regular pyramid, of which another regular pyramid with the same base and lesser height is removed at its base and is concave. An N-sided polygon as the base of the pyramid, It has 2N isosceles triangular faces. Also, It has N+2 vertices and 3N edges.

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

Total Surface Area of Hollow Pyramid given Inner Height and Total Height calculator 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 calculate 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 calculate Total Surface Area of Hollow Pyramid given Inner Height and Total Height using this online calculator? To use this online calculator 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. Here is how the Total Surface Area of Hollow Pyramid given Inner Height and Total Height calculation can be explained with given input values -> 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))).

FAQ

What is Total Surface Area of Hollow Pyramid given Inner Height and Total Height?

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 and is represented as TSA = n*l_e(Base)/2*(sqrt(h_Total^2+(l_e(Base)^2/4*(cot(pi/n))^2))+sqrt((h_Total-h_Inner)^2+(l_e(Base)^2/4*(cot(pi/n))^2))) or 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))). Number of Base Vertices of Hollow Pyramid are the number of base vertices of a regular 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, 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 & 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.

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

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 is calculated using 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 calculate Total Surface Area of Hollow Pyramid given Inner Height and Total Height, you need 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). With our tool, you need to enter the respective value for Number of Base Vertices of Hollow Pyramid, Edge Length of Base of Hollow Pyramid, Total Height of Hollow Pyramid & Inner Height of Hollow Pyramid and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Total Surface Area of Hollow Pyramid?

In this formula, Total Surface Area of Hollow Pyramid uses Number of Base Vertices of Hollow Pyramid, Edge Length of Base of Hollow Pyramid, Total Height of Hollow Pyramid & Inner Height of Hollow Pyramid. We can use 2 other way(s) to calculate the same, which is/are as follows -

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)))

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