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Total Surface Area of Frustum of Cone given Volume Formula

GoTotal Surface Area of Frustum of Cone given Slant Height Formula

GoTotal Surface Area of Frustum of Cone Formula

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

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

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

Total Surface Area of Frustum of Cone given Volume Example

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

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

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

844.6858 = 3.1416 \cdot (((10 + 5) \cdot \sqrt{{(\frac{3 \cdot 1500}{3.1416 \cdot (10^{2} + 5^{2} + (10 \cdot 5))})}^{2} + {(10 - 5)}^{2}}) + 10^{2} + 5^{2})

844.6858m² = 3.1416 \cdot (((10m + 5m) \cdot \sqrt{{(\frac{3 \cdot 1500m³}{3.1416 \cdot ({10m}^{2} + {5m}^{2} + (10m \cdot 5m))})}^{2} + {(10m - 5m)}^{2}}) + {10m}^{2} + {5m}^{2})

844.6858 = 3.1416 \cdot (((10 + 5) \cdot \sqrt{{(\frac{3 \cdot 1500}{3.1416 \cdot (10^{2} + 5^{2} + (10 \cdot 5))})}^{2} + {(10 - 5)}^{2}}) + 10^{2} + 5^{2})

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Total Surface Area of Frustum of Cone given Volume Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

TSA = π \cdot (((10m + 5m) \cdot \sqrt{{(\frac{3 \cdot 1500m³}{π \cdot ({10m}^{2} + {5m}^{2} + (10m \cdot 5m))})}^{2} + {(10m - 5m)}^{2}}) + {10m}^{2} + {5m}^{2})

Next Step Substitute values of Constants

∴

TSA = 3.1416 \cdot (((10m + 5m) \cdot \sqrt{{(\frac{3 \cdot 1500m³}{3.1416 \cdot ({10m}^{2} + {5m}^{2} + (10m \cdot 5m))})}^{2} + {(10m - 5m)}^{2}}) + {10m}^{2} + {5m}^{2})

Next Step Prepare to Evaluate

∴

TSA = 3.1416 \cdot (((10 + 5) \cdot \sqrt{{(\frac{3 \cdot 1500}{3.1416 \cdot (10^{2} + 5^{2} + (10 \cdot 5))})}^{2} + {(10 - 5)}^{2}}) + 10^{2} + 5^{2})

Next Step Evaluate

∴

TSA = 844.685845841447m²

LAST Step Rounding Answer

∴

TSA = 844.6858m²

Total Surface Area of Frustum of Cone given Volume Formula Elements

Variables

Constants

Functions

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

Volume of Frustum of Cone

Volume of Frustum of Cone is the quantity of three-dimensional space enclosed by the entire surface of the Frustum of the Cone.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume 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 Total Surface Area of Frustum of Cone

Go Total Surface Area of Frustum of Cone given Slant Height

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

Go Total Surface Area of Frustum of Cone

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

Go Total Surface Area of Frustum of Cone given Curved Surface Area

TSA = CSA + (π \cdot ({r Top}^{2} + {r Base}^{2}))

Other formulas in Total Surface Area of Frustum of Cone category

Go Base Area of Frustum of Cone

A Base = π \cdot {r Base}^{2}

Go Top Area of Frustum of Cone

A Top = π \cdot {r Top}^{2}

Go Curved Surface Area of Frustum of Cone

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

Go Curved Surface Area of Frustum of Cone given Slant Height

CSA = π \cdot (r Top + r Base) \cdot h Slant

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

Total Surface Area of Frustum of Cone given Volume evaluator uses Total Surface Area of Frustum of Cone = pi*(((Top Radius of Frustum of Cone+Base Radius of Frustum of Cone)*sqrt(((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))))^2+(Top Radius of Frustum of Cone-Base Radius of Frustum of Cone)^2))+Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2) to evaluate the Total Surface Area of Frustum of Cone, The Total Surface Area of Frustum of Cone given Volume formula is defined as the total quantity of plane enclosed on the entire surface of the Frustum of Cone, calculated using the volume, top radius and base radius of the Frustum of Cone. Total Surface Area of Frustum of Cone is denoted by TSA symbol.

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

FAQs on Total Surface Area of Frustum of Cone given Volume

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

The formula of Total Surface Area of Frustum of Cone given Volume is expressed as Total Surface Area of Frustum of Cone = pi*(((Top Radius of Frustum of Cone+Base Radius of Frustum of Cone)*sqrt(((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))))^2+(Top Radius of Frustum of Cone-Base Radius of Frustum of Cone)^2))+Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2). Here is an example- 844.6858 = pi*(((10+5)*sqrt(((3*1500)/(pi*(10^2+5^2+(10*5))))^2+(10-5)^2))+10^2+5^2).

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

With Top Radius of Frustum of Cone (r_Top), Base Radius of Frustum of Cone (r_Base) & Volume of Frustum of Cone (V) we can find Total Surface Area of Frustum of Cone given Volume using the formula - Total Surface Area of Frustum of Cone = pi*(((Top Radius of Frustum of Cone+Base Radius of Frustum of Cone)*sqrt(((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))))^2+(Top Radius of Frustum of Cone-Base Radius of Frustum of Cone)^2))+Top Radius of Frustum of Cone^2+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 Total Surface Area of Frustum of Cone?

Here are the different ways to Calculate Total Surface Area of Frustum of Cone-

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

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

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

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

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

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Total Surface Area of Frustum of Cone given Volume Formula

​GoTotal Surface Area of Frustum of Cone given Slant Height Formula

​GoTotal Surface Area of Frustum of Cone Formula

Total Surface Area of Frustum of Cone given Volume Example

Total Surface Area of Frustum of Cone given Volume Solution

Total Surface Area of Frustum of Cone given Volume Formula Elements

Other Formulas to find Total Surface Area of Frustum of Cone

Other formulas in Total Surface Area of Frustum of Cone category

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

FAQs on Total Surface Area of Frustum of Cone given Volume

Variable Name

GoTotal Surface Area of Frustum of Cone given Slant Height Formula

GoTotal Surface Area of Frustum of Cone Formula