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Height of Frustum of Cone given Total Surface Area Formula

GoHeight of Frustum of Cone given Slant Height Formula

GoHeight of Frustum of Cone given Curved Surface Area Formula

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Height of Frustum of Cone is the maximum vertical distance from the bottom to the top circular face of the Frustum of the Cone. Check FAQs

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

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

Height of Frustum of Cone given Total Surface Area Example

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

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

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

8.317 = \sqrt{{(\frac{\frac{850}{3.1416} - (10^{2} + 5^{2})}{10 + 5})}^{2} - {(10 - 5)}^{2}}

8.317m = \sqrt{{(\frac{\frac{850m²}{3.1416} - ({10m}^{2} + {5m}^{2})}{10m + 5m})}^{2} - {(10m - 5m)}^{2}}

8.317 = \sqrt{{(\frac{\frac{850}{3.1416} - (10^{2} + 5^{2})}{10 + 5})}^{2} - {(10 - 5)}^{2}}

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Height of Frustum of Cone given Total Surface Area Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

h = \sqrt{{(\frac{\frac{850m²}{π} - ({10m}^{2} + {5m}^{2})}{10m + 5m})}^{2} - {(10m - 5m)}^{2}}

Next Step Substitute values of Constants

∴

h = \sqrt{{(\frac{\frac{850m²}{3.1416} - ({10m}^{2} + {5m}^{2})}{10m + 5m})}^{2} - {(10m - 5m)}^{2}}

Next Step Prepare to Evaluate

∴

h = \sqrt{{(\frac{\frac{850}{3.1416} - (10^{2} + 5^{2})}{10 + 5})}^{2} - {(10 - 5)}^{2}}

Next Step Evaluate

∴

h = 8.31697176929561m

LAST Step Rounding Answer

∴

h = 8.317m

Height of Frustum of Cone given Total Surface Area Formula Elements

Variables

Constants

Functions

Height of Frustum of Cone

Height of Frustum of Cone is the maximum vertical distance from the bottom to the top circular face of the Frustum of the Cone.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Frustum of Cone

Total Surface Area of Frustum of Cone

Total Surface Area of Frustum of Cone is the total quantity of plane enclosed on the entire surface of the Frustum of the Cone.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Frustum of Cone

Top Radius of Frustum of Cone

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

Symbol: r_Top

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Top Radius of Frustum of Cone

Base Radius of Frustum of Cone

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

Symbol: r_Base

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Base Radius of Frustum of 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 Frustum of Cone

Go Height of Frustum of Cone given Slant Height

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

Go Height of Frustum of Cone given Curved Surface Area

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

Go Height of Frustum of Cone given Volume

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

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

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

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

FAQs on Height of Frustum of Cone given Total Surface Area

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

The formula of Height of Frustum of Cone given Total Surface Area is expressed as Height of Frustum of Cone = sqrt(((Total Surface Area of Frustum of Cone/pi-(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2))/(Top Radius of Frustum of Cone+Base Radius of Frustum of Cone))^2-(Top Radius of Frustum of Cone-Base Radius of Frustum of Cone)^2). Here is an example- 8.316972 = sqrt(((850/pi-(10^2+5^2))/(10+5))^2-(10-5)^2).

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

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

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

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

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

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

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

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

Height of Frustum of 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 Frustum of Cone given Total Surface Area can be measured.

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Height of Frustum of Cone given Total Surface Area Formula

​GoHeight of Frustum of Cone given Slant Height Formula

​GoHeight of Frustum of Cone given Curved Surface Area Formula

Height of Frustum of Cone given Total Surface Area Example

Height of Frustum of Cone given Total Surface Area Solution

Height of Frustum of Cone given Total Surface Area Formula Elements

Other Formulas to find Height of Frustum of Cone

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

FAQs on Height of Frustum of Cone given Total Surface Area

Variable Name

GoHeight of Frustum of Cone given Slant Height Formula

GoHeight of Frustum of Cone given Curved Surface Area Formula