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Total Surface Area of Regular Bipyramid given Volume and Half Height Formula

GoTotal Surface Area of Regular Bipyramid Formula

GoTotal Surface Area of Regular Bipyramid given Volume Formula

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

TSA = n \cdot \sqrt{\frac{4 \cdot V \cdot \tan (\frac{π}{n})}{\frac{2}{3} \cdot n \cdot h Half}} \cdot \sqrt{{h Half}^{2} + (\frac{V \cdot \tan (\frac{π}{n})}{\frac{2}{3} \cdot n \cdot h Half} \cdot {(\cot (\frac{π}{n}))}^{2})}

TSA - Total Surface Area of Regular Bipyramid?n - Number of Base Vertices of Regular Bipyramid?V - Volume of Regular Bipyramid?h_Half - Half Height of Regular Bipyramid?π - Archimedes' constant?

Total Surface Area of Regular Bipyramid given Volume and Half Height Example

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Here is how the Total Surface Area of Regular Bipyramid given Volume and Half Height equation looks like with Values.

Here is how the Total Surface Area of Regular Bipyramid given Volume and Half Height equation looks like with Units.

Here is how the Total Surface Area of Regular Bipyramid given Volume and Half Height equation looks like.

335.848 = 4 \cdot \sqrt{\frac{4 \cdot 450 \cdot \tan (\frac{3.1416}{4})}{\frac{2}{3} \cdot 4 \cdot 7}} \cdot \sqrt{7^{2} + (\frac{450 \cdot \tan (\frac{3.1416}{4})}{\frac{2}{3} \cdot 4 \cdot 7} \cdot {(\cot (\frac{3.1416}{4}))}^{2})}

335.848m² = 4 \cdot \sqrt{\frac{4 \cdot 450m³ \cdot \tan (\frac{3.1416}{4})}{\frac{2}{3} \cdot 4 \cdot 7m}} \cdot \sqrt{{7m}^{2} + (\frac{450m³ \cdot \tan (\frac{3.1416}{4})}{\frac{2}{3} \cdot 4 \cdot 7m} \cdot {(\cot (\frac{3.1416}{4}))}^{2})}

335.848 = 4 \cdot \sqrt{\frac{4 \cdot 450 \cdot \tan (\frac{3.1416}{4})}{\frac{2}{3} \cdot 4 \cdot 7}} \cdot \sqrt{7^{2} + (\frac{450 \cdot \tan (\frac{3.1416}{4})}{\frac{2}{3} \cdot 4 \cdot 7} \cdot {(\cot (\frac{3.1416}{4}))}^{2})}

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Total Surface Area of Regular Bipyramid given Volume and Half Height Solution

Follow our step by step solution on how to calculate Total Surface Area of Regular Bipyramid given Volume and Half Height?

FIRST Step Consider the formula

TSA = n \cdot \sqrt{\frac{4 \cdot V \cdot \tan (\frac{π}{n})}{\frac{2}{3} \cdot n \cdot h Half}} \cdot \sqrt{{h Half}^{2} + (\frac{V \cdot \tan (\frac{π}{n})}{\frac{2}{3} \cdot n \cdot h Half} \cdot {(\cot (\frac{π}{n}))}^{2})}

Next Step Substitute values of Variables

∴

TSA = 4 \cdot \sqrt{\frac{4 \cdot 450m³ \cdot \tan (\frac{π}{4})}{\frac{2}{3} \cdot 4 \cdot 7m}} \cdot \sqrt{{7m}^{2} + (\frac{450m³ \cdot \tan (\frac{π}{4})}{\frac{2}{3} \cdot 4 \cdot 7m} \cdot {(\cot (\frac{π}{4}))}^{2})}

Next Step Substitute values of Constants

∴

TSA = 4 \cdot \sqrt{\frac{4 \cdot 450m³ \cdot \tan (\frac{3.1416}{4})}{\frac{2}{3} \cdot 4 \cdot 7m}} \cdot \sqrt{{7m}^{2} + (\frac{450m³ \cdot \tan (\frac{3.1416}{4})}{\frac{2}{3} \cdot 4 \cdot 7m} \cdot {(\cot (\frac{3.1416}{4}))}^{2})}

Next Step Prepare to Evaluate

∴

TSA = 4 \cdot \sqrt{\frac{4 \cdot 450 \cdot \tan (\frac{3.1416}{4})}{\frac{2}{3} \cdot 4 \cdot 7}} \cdot \sqrt{7^{2} + (\frac{450 \cdot \tan (\frac{3.1416}{4})}{\frac{2}{3} \cdot 4 \cdot 7} \cdot {(\cot (\frac{3.1416}{4}))}^{2})}

Next Step Evaluate

∴

TSA = 335.847997687973m²

LAST Step Rounding Answer

∴

TSA = 335.848m²

Total Surface Area of Regular Bipyramid given Volume and Half Height Formula Elements

Variables

Constants

Functions

Total Surface Area of Regular Bipyramid

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

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Regular Bipyramid

Number of Base Vertices of Regular Bipyramid

Number of Base Vertices of Regular Bipyramid are the number of base vertices of a Regular Bipyramid.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be greater than 2.99.

Formulas to find Number of Base Vertices of Regular Bipyramid

Volume of Regular Bipyramid

Volume of Regular Bipyramid is the total quantity of three-dimensional space enclosed by the surface of the Regular Bipyramid.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Regular Bipyramid

Half Height of Regular Bipyramid

Half Height of Regular Bipyramid is the total length of the perpendicular from the apex to the base of any one of the pyramids in the Regular Bipyramid.

Symbol: h_Half

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Half Height of Regular Bipyramid

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 Total Surface Area of Regular Bipyramid

Go Total Surface Area of Regular Bipyramid

TSA = n \cdot l e(Base) \cdot \sqrt{{h Half}^{2} + (\frac{1}{4} \cdot {l e(Base)}^{2} \cdot {(\cot (\frac{π}{n}))}^{2})}

Go Total Surface Area of Regular Bipyramid given Volume

TSA = n \cdot l e(Base) \cdot \sqrt{{(\frac{4 \cdot V \cdot \tan (\frac{π}{n})}{\frac{2}{3} \cdot n \cdot {l e(Base)}^{2}})}^{2} + (\frac{1}{4} \cdot {l e(Base)}^{2} \cdot {(\cot (\frac{π}{n}))}^{2})}

Go Total Surface Area of Regular Bipyramid given Total Height

TSA = n \cdot l e(Base) \cdot \sqrt{{(\frac{h Total}{2})}^{2} + (\frac{1}{4} \cdot {l e(Base)}^{2} \cdot {(\cot (\frac{π}{n}))}^{2})}

How to Evaluate Total Surface Area of Regular Bipyramid given Volume and Half Height?

Total Surface Area of Regular Bipyramid given Volume and Half Height evaluator uses Total Surface Area of Regular Bipyramid = Number of Base Vertices of Regular Bipyramid*sqrt((4*Volume of Regular Bipyramid*tan(pi/Number of Base Vertices of Regular Bipyramid))/(2/3*Number of Base Vertices of Regular Bipyramid*Half Height of Regular Bipyramid))*sqrt(Half Height of Regular Bipyramid^2+((Volume of Regular Bipyramid*tan(pi/Number of Base Vertices of Regular Bipyramid))/(2/3*Number of Base Vertices of Regular Bipyramid*Half Height of Regular Bipyramid)*(cot(pi/Number of Base Vertices of Regular Bipyramid))^2)) to evaluate the Total Surface Area of Regular Bipyramid, Total Surface Area of Regular Bipyramid given Volume and Half Height formula is defined as the total amount of two-dimensional space occupied by all the faces of the Regular Bipyramid and is calculated using the volume and half height of the Regular Bipyramid. Total Surface Area of Regular Bipyramid is denoted by TSA symbol.

How to evaluate Total Surface Area of Regular Bipyramid given Volume and Half Height using this online evaluator? To use this online evaluator for Total Surface Area of Regular Bipyramid given Volume and Half Height, enter Number of Base Vertices of Regular Bipyramid (n), Volume of Regular Bipyramid (V) & Half Height of Regular Bipyramid (h_Half) and hit the calculate button.

FAQs on Total Surface Area of Regular Bipyramid given Volume and Half Height

What is the formula to find Total Surface Area of Regular Bipyramid given Volume and Half Height?

The formula of Total Surface Area of Regular Bipyramid given Volume and Half Height is expressed as Total Surface Area of Regular Bipyramid = Number of Base Vertices of Regular Bipyramid*sqrt((4*Volume of Regular Bipyramid*tan(pi/Number of Base Vertices of Regular Bipyramid))/(2/3*Number of Base Vertices of Regular Bipyramid*Half Height of Regular Bipyramid))*sqrt(Half Height of Regular Bipyramid^2+((Volume of Regular Bipyramid*tan(pi/Number of Base Vertices of Regular Bipyramid))/(2/3*Number of Base Vertices of Regular Bipyramid*Half Height of Regular Bipyramid)*(cot(pi/Number of Base Vertices of Regular Bipyramid))^2)). Here is an example- 335.848 = 4*sqrt((4*450*tan(pi/4))/(2/3*4*7))*sqrt(7^2+((450*tan(pi/4))/(2/3*4*7)*(cot(pi/4))^2)).

How to calculate Total Surface Area of Regular Bipyramid given Volume and Half Height?

With Number of Base Vertices of Regular Bipyramid (n), Volume of Regular Bipyramid (V) & Half Height of Regular Bipyramid (h_Half) we can find Total Surface Area of Regular Bipyramid given Volume and Half Height using the formula - Total Surface Area of Regular Bipyramid = Number of Base Vertices of Regular Bipyramid*sqrt((4*Volume of Regular Bipyramid*tan(pi/Number of Base Vertices of Regular Bipyramid))/(2/3*Number of Base Vertices of Regular Bipyramid*Half Height of Regular Bipyramid))*sqrt(Half Height of Regular Bipyramid^2+((Volume of Regular Bipyramid*tan(pi/Number of Base Vertices of Regular Bipyramid))/(2/3*Number of Base Vertices of Regular Bipyramid*Half Height of Regular Bipyramid)*(cot(pi/Number of Base Vertices of Regular Bipyramid))^2)). This formula also uses Archimedes' constant and , Tangent (tan), Cotangent (cot), Square Root (sqrt) function(s).

What are the other ways to Calculate Total Surface Area of Regular Bipyramid?

Here are the different ways to Calculate Total Surface Area of Regular Bipyramid-

Total Surface Area of Regular Bipyramid=Number of Base Vertices of Regular Bipyramid*Edge Length of Base of Regular Bipyramid*sqrt(Half Height of Regular Bipyramid^2+(1/4*Edge Length of Base of Regular Bipyramid^2*(cot(pi/Number of Base Vertices of Regular Bipyramid))^2))
Total Surface Area of Regular Bipyramid=Number of Base Vertices of Regular Bipyramid*Edge Length of Base of Regular Bipyramid*sqrt(((4*Volume of Regular Bipyramid*tan(pi/Number of Base Vertices of Regular Bipyramid))/(2/3*Number of Base Vertices of Regular Bipyramid*Edge Length of Base of Regular Bipyramid^2))^2+(1/4*Edge Length of Base of Regular Bipyramid^2*(cot(pi/Number of Base Vertices of Regular Bipyramid))^2))
Total Surface Area of Regular Bipyramid=Number of Base Vertices of Regular Bipyramid*Edge Length of Base of Regular Bipyramid*sqrt((Total Height of Regular Bipyramid/2)^2+(1/4*Edge Length of Base of Regular Bipyramid^2*(cot(pi/Number of Base Vertices of Regular Bipyramid))^2))

Can the Total Surface Area of Regular Bipyramid given Volume and Half Height be negative?

No, the Total Surface Area of Regular Bipyramid given Volume and Half Height, measured in Area cannot be negative.

Which unit is used to measure Total Surface Area of Regular Bipyramid given Volume and Half Height?

Total Surface Area of Regular Bipyramid given Volume and Half 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 Regular Bipyramid given Volume and Half Height can be measured.

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Total Surface Area of Regular Bipyramid given Volume and Half Height Formula

​GoTotal Surface Area of Regular Bipyramid Formula

​GoTotal Surface Area of Regular Bipyramid given Volume Formula

Total Surface Area of Regular Bipyramid given Volume and Half Height Example

Total Surface Area of Regular Bipyramid given Volume and Half Height Solution

Total Surface Area of Regular Bipyramid given Volume and Half Height Formula Elements

Other Formulas to find Total Surface Area of Regular Bipyramid

How to Evaluate Total Surface Area of Regular Bipyramid given Volume and Half Height?

FAQs on Total Surface Area of Regular Bipyramid given Volume and Half Height

Variable Name

GoTotal Surface Area of Regular Bipyramid Formula

GoTotal Surface Area of Regular Bipyramid given Volume Formula