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Total Surface Area of Frustum of Cone given Volume and Base Area Formula

GoTotal Surface Area of Frustum of Cone given Slant Height, Base Area and Top Area Formula

GoTotal Surface Area of Frustum of Cone given Slant Height, Height and Base Area 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 + \sqrt{\frac{A Base}{π}}) \cdot \sqrt{{(\frac{3 \cdot V}{π \cdot ({r Top}^{2} + \frac{A Base}{π} + (r Top \cdot \sqrt{\frac{A Base}{π}}))})}^{2} + {(r Top - \sqrt{\frac{A Base}{π}})}^{2}}) + {r Top}^{2} + \frac{A Base}{π})

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

Total Surface Area of Frustum of Cone given Volume and Base Area Example

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

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

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

844.6602 = 3.1416 \cdot (((10 + \sqrt{\frac{80}{3.1416}}) \cdot \sqrt{{(\frac{3 \cdot 1500}{3.1416 \cdot (10^{2} + \frac{80}{3.1416} + (10 \cdot \sqrt{\frac{80}{3.1416}}))})}^{2} + {(10 - \sqrt{\frac{80}{3.1416}})}^{2}}) + 10^{2} + \frac{80}{3.1416})

844.6602m² = 3.1416 \cdot (((10m + \sqrt{\frac{80m²}{3.1416}}) \cdot \sqrt{{(\frac{3 \cdot 1500m³}{3.1416 \cdot ({10m}^{2} + \frac{80m²}{3.1416} + (10m \cdot \sqrt{\frac{80m²}{3.1416}}))})}^{2} + {(10m - \sqrt{\frac{80m²}{3.1416}})}^{2}}) + {10m}^{2} + \frac{80m²}{3.1416})

844.6602 = 3.1416 \cdot (((10 + \sqrt{\frac{80}{3.1416}}) \cdot \sqrt{{(\frac{3 \cdot 1500}{3.1416 \cdot (10^{2} + \frac{80}{3.1416} + (10 \cdot \sqrt{\frac{80}{3.1416}}))})}^{2} + {(10 - \sqrt{\frac{80}{3.1416}})}^{2}}) + 10^{2} + \frac{80}{3.1416})

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Total Surface Area of Frustum of Cone given Volume and Base Area Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

TSA = π \cdot (((10m + \sqrt{\frac{80m²}{π}}) \cdot \sqrt{{(\frac{3 \cdot 1500m³}{π \cdot ({10m}^{2} + \frac{80m²}{π} + (10m \cdot \sqrt{\frac{80m²}{π}}))})}^{2} + {(10m - \sqrt{\frac{80m²}{π}})}^{2}}) + {10m}^{2} + \frac{80m²}{π})

Next Step Substitute values of Constants

∴

TSA = 3.1416 \cdot (((10m + \sqrt{\frac{80m²}{3.1416}}) \cdot \sqrt{{(\frac{3 \cdot 1500m³}{3.1416 \cdot ({10m}^{2} + \frac{80m²}{3.1416} + (10m \cdot \sqrt{\frac{80m²}{3.1416}}))})}^{2} + {(10m - \sqrt{\frac{80m²}{3.1416}})}^{2}}) + {10m}^{2} + \frac{80m²}{3.1416})

Next Step Prepare to Evaluate

∴

TSA = 3.1416 \cdot (((10 + \sqrt{\frac{80}{3.1416}}) \cdot \sqrt{{(\frac{3 \cdot 1500}{3.1416 \cdot (10^{2} + \frac{80}{3.1416} + (10 \cdot \sqrt{\frac{80}{3.1416}}))})}^{2} + {(10 - \sqrt{\frac{80}{3.1416}})}^{2}}) + 10^{2} + \frac{80}{3.1416})

Next Step Evaluate

∴

TSA = 844.660204255666m²

LAST Step Rounding Answer

∴

TSA = 844.6602m²

Total Surface Area of Frustum of Cone given Volume and Base Area 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 Area of Frustum of Cone

The Base Area of Frustum of Cone is the total amount of two-dimensional space occupied by the base face of the Frustum of the Cone.

Symbol: A_Base

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Base Area 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, Base Area and Top Area

TSA = (π \cdot (\sqrt{\frac{A Top}{π}} + \sqrt{\frac{A Base}{π}}) \cdot h Slant) + A Top + A Base

Go Total Surface Area of Frustum of Cone given Slant Height, Height and Base Area

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

Go Total Surface Area of Frustum of Cone given Slant Height, Height and Base Radius

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

Go Total Surface Area of Frustum of Cone given Slant Height, Height and Top Radius

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

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

Total Surface Area of Frustum of Cone given Volume and Base Area evaluator uses Total Surface Area of Frustum of Cone = pi*(((Top Radius of Frustum of Cone+sqrt(Base Area of Frustum of Cone/pi))*sqrt(((3*Volume of Frustum of Cone)/(pi*(Top Radius of Frustum of Cone^2+Base Area of Frustum of Cone/pi+(Top Radius of Frustum of Cone*sqrt(Base Area of Frustum of Cone/pi)))))^2+(Top Radius of Frustum of Cone-sqrt(Base Area of Frustum of Cone/pi))^2))+Top Radius of Frustum of Cone^2+Base Area of Frustum of Cone/pi) to evaluate the Total Surface Area of Frustum of Cone, The Total Surface Area of Frustum of Cone given Volume and Base Area 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 area 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 and Base Area using this online evaluator? To use this online evaluator for Total Surface Area of Frustum of Cone given Volume and Base Area, enter Top Radius of Frustum of Cone (r_Top), Base Area of Frustum of Cone (A_Base) & Volume of Frustum of Cone (V) and hit the calculate button.

FAQs on Total Surface Area of Frustum of Cone given Volume and Base Area

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

The formula of Total Surface Area of Frustum of Cone given Volume and Base Area is expressed as Total Surface Area of Frustum of Cone = pi*(((Top Radius of Frustum of Cone+sqrt(Base Area of Frustum of Cone/pi))*sqrt(((3*Volume of Frustum of Cone)/(pi*(Top Radius of Frustum of Cone^2+Base Area of Frustum of Cone/pi+(Top Radius of Frustum of Cone*sqrt(Base Area of Frustum of Cone/pi)))))^2+(Top Radius of Frustum of Cone-sqrt(Base Area of Frustum of Cone/pi))^2))+Top Radius of Frustum of Cone^2+Base Area of Frustum of Cone/pi). Here is an example- 844.6602 = pi*(((10+sqrt(80/pi))*sqrt(((3*1500)/(pi*(10^2+80/pi+(10*sqrt(80/pi)))))^2+(10-sqrt(80/pi))^2))+10^2+80/pi).

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

With Top Radius of Frustum of Cone (r_Top), Base Area of Frustum of Cone (A_Base) & Volume of Frustum of Cone (V) we can find Total Surface Area of Frustum of Cone given Volume and Base Area using the formula - Total Surface Area of Frustum of Cone = pi*(((Top Radius of Frustum of Cone+sqrt(Base Area of Frustum of Cone/pi))*sqrt(((3*Volume of Frustum of Cone)/(pi*(Top Radius of Frustum of Cone^2+Base Area of Frustum of Cone/pi+(Top Radius of Frustum of Cone*sqrt(Base Area of Frustum of Cone/pi)))))^2+(Top Radius of Frustum of Cone-sqrt(Base Area of Frustum of Cone/pi))^2))+Top Radius of Frustum of Cone^2+Base Area of Frustum of Cone/pi). 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*(sqrt(Top Area of Frustum of Cone/pi)+sqrt(Base Area of Frustum of Cone/pi))*Slant Height of Frustum of Cone)+Top Area of Frustum of Cone+Base Area of Frustum of Cone
Total Surface Area of Frustum of Cone=pi*(((sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)+2*sqrt(Base Area of Frustum of Cone/pi))*Slant Height of Frustum of Cone)+(sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)+sqrt(Base Area of Frustum of Cone/pi))^2)+Base Area of Frustum of Cone
Total Surface Area of Frustum of Cone=pi*(((sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)+2*Base Radius of Frustum of Cone)*Slant Height of Frustum of Cone)+(sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)+Base Radius of Frustum of Cone)^2+Base Radius of Frustum of Cone^2)

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

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

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

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

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Total Surface Area of Frustum of Cone given Volume and Base Area Formula

​GoTotal Surface Area of Frustum of Cone given Slant Height, Base Area and Top Area Formula

​GoTotal Surface Area of Frustum of Cone given Slant Height, Height and Base Area Formula

Total Surface Area of Frustum of Cone given Volume and Base Area Example

Total Surface Area of Frustum of Cone given Volume and Base Area Solution

Total Surface Area of Frustum of Cone given Volume and Base Area Formula Elements

Other Formulas to find Total Surface Area of Frustum of Cone

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

FAQs on Total Surface Area of Frustum of Cone given Volume and Base Area

Variable Name

GoTotal Surface Area of Frustum of Cone given Slant Height, Base Area and Top Area Formula

GoTotal Surface Area of Frustum of Cone given Slant Height, Height and Base Area Formula