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Height of Truncated Cone given Total Surface Area Formula

GoHeight of Truncated Cone given Slant Height Formula

GoHeight of Truncated Cone given Volume Formula

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Height of Truncated Cone is the vertical distance from the base circular surface to the top most point of the Truncated Cone. Check FAQs

h = \sqrt{{(\frac{TSA - π \cdot ({r Base}^{2} + {r Top}^{2})}{π \cdot (r Base + r Top)})}^{2} - {(r Base - r Top)}^{2}}

h - Height of Truncated Cone?TSA - Total Surface Area of Truncated Cone?r_Base - Base Radius of Truncated Cone?r_Top - Top Radius of Truncated Cone?π - Archimedes' constant?

Height of Truncated Cone given Total Surface Area Example

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Here is how the Height of Truncated Cone given Total Surface Area equation looks like with Values.

Here is how the Height of Truncated Cone given Total Surface Area equation looks like with Units.

Here is how the Height of Truncated Cone given Total Surface Area equation looks like.

7.0699 = \sqrt{{(\frac{260 - 3.1416 \cdot (5^{2} + 2^{2})}{3.1416 \cdot (5 + 2)})}^{2} - {(5 - 2)}^{2}}

7.0699m = \sqrt{{(\frac{260m² - 3.1416 \cdot ({5m}^{2} + {2m}^{2})}{3.1416 \cdot (5m + 2m)})}^{2} - {(5m - 2m)}^{2}}

7.0699 = \sqrt{{(\frac{260 - 3.1416 \cdot (5^{2} + 2^{2})}{3.1416 \cdot (5 + 2)})}^{2} - {(5 - 2)}^{2}}

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Height of Truncated Cone given Total Surface Area Solution

Follow our step by step solution on how to calculate Height of Truncated Cone given Total Surface Area?

FIRST Step Consider the formula

h = \sqrt{{(\frac{TSA - π \cdot ({r Base}^{2} + {r Top}^{2})}{π \cdot (r Base + r Top)})}^{2} - {(r Base - r Top)}^{2}}

Next Step Substitute values of Variables

∴

h = \sqrt{{(\frac{260m² - π \cdot ({5m}^{2} + {2m}^{2})}{π \cdot (5m + 2m)})}^{2} - {(5m - 2m)}^{2}}

Next Step Substitute values of Constants

∴

h = \sqrt{{(\frac{260m² - 3.1416 \cdot ({5m}^{2} + {2m}^{2})}{3.1416 \cdot (5m + 2m)})}^{2} - {(5m - 2m)}^{2}}

Next Step Prepare to Evaluate

∴

h = \sqrt{{(\frac{260 - 3.1416 \cdot (5^{2} + 2^{2})}{3.1416 \cdot (5 + 2)})}^{2} - {(5 - 2)}^{2}}

Next Step Evaluate

∴

h = 7.06991171403825m

LAST Step Rounding Answer

∴

h = 7.0699m

Height of Truncated Cone given Total Surface Area Formula Elements

Variables

Constants

Functions

Height of Truncated Cone

Height of Truncated Cone is the vertical distance from the base circular surface to the top most point of the Truncated Cone.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Truncated Cone

Total Surface Area of Truncated Cone

Total Surface Area of Truncated Cone is the quantity of plane enclosed by the entire surface of the Truncated Cone.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Truncated Cone

Base Radius of Truncated Cone

Base Radius of Truncated Cone is the distance between the center and any point on the circumference of the base circular surface of the Truncated Cone.

Symbol: r_Base

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Base Radius of Truncated Cone

Top Radius of Truncated Cone

Top Radius of Truncated Cone is the distance between the center and any point on the circumference of the top circular surface of the Truncated Cone.

Symbol: r_Top

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Top Radius of Truncated Cone

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

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 Height of Truncated Cone

Go Height of Truncated Cone given Slant Height

h = \sqrt{{h Slant}^{2} - {(r Base - r Top)}^{2}}

Go Height of Truncated Cone given Volume

h = \frac{3 \cdot V}{π \cdot ({r Base}^{2} + (r Base \cdot r Top) + {r Top}^{2})}

Go Height of Truncated Cone given Curved Surface Area

h = \sqrt{{(\frac{CSA}{π \cdot (r Base + r Top)})}^{2} - {(r Base - r Top)}^{2}}

How to Evaluate Height of Truncated Cone given Total Surface Area?

Height of Truncated Cone given Total Surface Area evaluator uses Height of Truncated Cone = sqrt(((Total Surface Area of Truncated Cone-pi*(Base Radius of Truncated Cone^2+Top Radius of Truncated Cone^2))/(pi*(Base Radius of Truncated Cone+Top Radius of Truncated Cone)))^2-(Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2) to evaluate the Height of Truncated Cone, The Height of Truncated Cone given Total Surface Area formula is defined as the vertical distance from the base circular surface to the top most point of the Truncated Cone, and calculated using the total surface area of Truncated Cone. Height of Truncated Cone is denoted by h symbol.

How to evaluate Height of Truncated Cone given Total Surface Area using this online evaluator? To use this online evaluator for Height of Truncated Cone given Total Surface Area, enter Total Surface Area of Truncated Cone (TSA), Base Radius of Truncated Cone (r_Base) & Top Radius of Truncated Cone (r_Top) and hit the calculate button.

FAQs on Height of Truncated Cone given Total Surface Area

What is the formula to find Height of Truncated Cone given Total Surface Area?

The formula of Height of Truncated Cone given Total Surface Area is expressed as Height of Truncated Cone = sqrt(((Total Surface Area of Truncated Cone-pi*(Base Radius of Truncated Cone^2+Top Radius of Truncated Cone^2))/(pi*(Base Radius of Truncated Cone+Top Radius of Truncated Cone)))^2-(Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2). Here is an example- 7.069912 = sqrt(((260-pi*(5^2+2^2))/(pi*(5+2)))^2-(5-2)^2).

How to calculate Height of Truncated Cone given Total Surface Area?

With Total Surface Area of Truncated Cone (TSA), Base Radius of Truncated Cone (r_Base) & Top Radius of Truncated Cone (r_Top) we can find Height of Truncated Cone given Total Surface Area using the formula - Height of Truncated Cone = sqrt(((Total Surface Area of Truncated Cone-pi*(Base Radius of Truncated Cone^2+Top Radius of Truncated Cone^2))/(pi*(Base Radius of Truncated Cone+Top Radius of Truncated Cone)))^2-(Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Height of Truncated Cone?

Here are the different ways to Calculate Height of Truncated Cone-

Height of Truncated Cone=sqrt(Slant Height of Truncated Cone^2-(Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2)
Height of Truncated Cone=(3*Volume of Truncated Cone)/(pi*(Base Radius of Truncated Cone^2+(Base Radius of Truncated Cone*Top Radius of Truncated Cone)+Top Radius of Truncated Cone^2))
Height of Truncated Cone=sqrt((Curved Surface Area of Truncated Cone/(pi*(Base Radius of Truncated Cone+Top Radius of Truncated Cone)))^2-(Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2)

Can the Height of Truncated Cone given Total Surface Area be negative?

No, the Height of Truncated Cone given Total Surface Area, measured in Length cannot be negative.

Which unit is used to measure Height of Truncated Cone given Total Surface Area?

Height of Truncated Cone given Total Surface Area is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Height of Truncated Cone given Total Surface Area can be measured.

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Height of Truncated Cone given Total Surface Area Formula

​GoHeight of Truncated Cone given Slant Height Formula

​GoHeight of Truncated Cone given Volume Formula

Height of Truncated Cone given Total Surface Area Example

Height of Truncated Cone given Total Surface Area Solution

Height of Truncated Cone given Total Surface Area Formula Elements

Other Formulas to find Height of Truncated Cone

How to Evaluate Height of Truncated Cone given Total Surface Area?

FAQs on Height of Truncated Cone given Total Surface Area

Variable Name

GoHeight of Truncated Cone given Slant Height Formula

GoHeight of Truncated Cone given Volume Formula