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

✖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.ⓘ Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner Height [R_A/V]

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

STEP 0: Pre-Calculation Summary

Formula Used

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)))
R_A/V = (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))))/((1/3*n*h_Inner*l_e(Base)^2)/(4*tan(pi/n)))
This formula uses 1 Constants, 3 Functions, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., 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., 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

Surface to Volume Ratio of Hollow Pyramid - (Measured in 1 per Meter) - 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.
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

R_A/V = (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))))/((1/3*n*h_Inner*l_e(Base)^2)/(4*tan(pi/n))) --> (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)))

Evaluating ... ...

R_A/V = 1.83102851759134

STEP 3: Convert Result to Output's Unit

1.83102851759134 1 per Meter --> No Conversion Required

FINAL ANSWER

1.83102851759134 ≈ 1.831029 1 per Meter <-- Surface to Volume Ratio of Hollow Pyramid

(Calculation completed in 00.004 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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< Surface to Volume Ratio of Hollow Pyramid Calculators

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

LaTeX Go 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)))

Surface to Volume Ratio of Hollow Pyramid

LaTeX Go 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 given Total Height and Inner Height

LaTeX Go 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)))

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

FAQ

What is 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 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 and is represented as R_A/V = (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))))/((1/3*n*h_Inner*l_e(Base)^2)/(4*tan(pi/n))) or 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))). 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 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 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 is calculated using 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 calculate Surface to Volume Ratio of Hollow Pyramid given Total Height and Inner 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 Surface to Volume Ratio of Hollow Pyramid?

In this formula, Surface to Volume Ratio 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 -

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)))

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