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Total Surface Area of Frustum of Cone given Slant Height, Height and Base Radius 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 (((\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})

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

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

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Here is how the Total Surface Area of Frustum of Cone given Slant Height, Height and Base Radius equation looks like.

739.3393 = 3.1416 \cdot (((\sqrt{9^{2} - 8^{2}} + 2 \cdot 5) \cdot 9) + {(\sqrt{9^{2} - 8^{2}} + 5)}^{2} + 5^{2})

739.3393m² = 3.1416 \cdot (((\sqrt{{9m}^{2} - {8m}^{2}} + 2 \cdot 5m) \cdot 9m) + {(\sqrt{{9m}^{2} - {8m}^{2}} + 5m)}^{2} + {5m}^{2})

739.3393 = 3.1416 \cdot (((\sqrt{9^{2} - 8^{2}} + 2 \cdot 5) \cdot 9) + {(\sqrt{9^{2} - 8^{2}} + 5)}^{2} + 5^{2})

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

Follow our step by step solution on how to calculate Total Surface Area of Frustum of Cone given Slant Height, Height and Base Radius?

FIRST Step Consider the formula

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})

Next Step Substitute values of Variables

∴

TSA = π \cdot (((\sqrt{{9m}^{2} - {8m}^{2}} + 2 \cdot 5m) \cdot 9m) + {(\sqrt{{9m}^{2} - {8m}^{2}} + 5m)}^{2} + {5m}^{2})

Next Step Substitute values of Constants

∴

TSA = 3.1416 \cdot (((\sqrt{{9m}^{2} - {8m}^{2}} + 2 \cdot 5m) \cdot 9m) + {(\sqrt{{9m}^{2} - {8m}^{2}} + 5m)}^{2} + {5m}^{2})

Next Step Prepare to Evaluate

∴

TSA = 3.1416 \cdot (((\sqrt{9^{2} - 8^{2}} + 2 \cdot 5) \cdot 9) + {(\sqrt{9^{2} - 8^{2}} + 5)}^{2} + 5^{2})

Next Step Evaluate

∴

TSA = 739.339295138486m²

LAST Step Rounding Answer

∴

TSA = 739.3393m²

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

Slant Height of Frustum of Cone

The Slant Height of Frustum of Cone is the length of the line segment joining the extremities of two parallel radii, drawn in the same direction of the two circular bases.

Symbol: h_Slant

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Slant Height of Frustum of Cone

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

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 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 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})

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

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

How to Evaluate Total Surface Area of Frustum of Cone given Slant Height, Height and Base Radius?

Total Surface Area of Frustum of Cone given Slant Height, Height and Base Radius evaluator uses 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) to evaluate the Total Surface Area of Frustum of Cone, The Total Surface Area of Frustum of Cone given Slant Height, Height and Base Radius formula is defined as the total quantity of plane enclosed on the entire surface of the Frustum of Cone, calculated using the slant height, height 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 Slant Height, Height and Base Radius using this online evaluator? To use this online evaluator for Total Surface Area of Frustum of Cone given Slant Height, Height and Base Radius, enter Slant Height of Frustum of Cone (h_Slant), Height of Frustum of Cone (h) & Base Radius of Frustum of Cone (r_Base) and hit the calculate button.

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

What is the formula to find Total Surface Area of Frustum of Cone given Slant Height, Height and Base Radius?

The formula of Total Surface Area of Frustum of Cone given Slant Height, Height and Base Radius is expressed as 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). Here is an example- 739.3393 = pi*(((sqrt(9^2-8^2)+2*5)*9)+(sqrt(9^2-8^2)+5)^2+5^2).

How to calculate Total Surface Area of Frustum of Cone given Slant Height, Height and Base Radius?

With Slant Height of Frustum of Cone (h_Slant), Height of Frustum of Cone (h) & Base Radius of Frustum of Cone (r_Base) we can find Total Surface Area of Frustum of Cone given Slant Height, Height and Base Radius using the formula - 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). 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*(((2*Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))*Slant Height of Frustum of Cone)+Top Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))^2)

Can the Total Surface Area of Frustum of Cone given Slant Height, Height and Base Radius be negative?

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

Which unit is used to measure Total Surface Area of Frustum of Cone given Slant Height, Height and Base Radius?

Total Surface Area of Frustum of Cone given Slant Height, Height and Base Radius 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 Slant Height, Height and Base Radius can be measured.

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

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

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

Other Formulas to find Total Surface Area of Frustum of Cone

How to Evaluate Total Surface Area of Frustum of Cone given Slant Height, Height and Base Radius?

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

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