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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(((2rTop-hSlant2-h2)hSlant)+rTop2+(rTop-hSlant2-h2)2)
TSA - Total Surface Area of Frustum of Cone?rTop - Top Radius of Frustum of Cone?hSlant - Slant Height of Frustum of Cone?h - Height of Frustum of Cone?π - Archimedes' constant?

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

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

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

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

871.5719Edit=3.1416(((210Edit-9Edit2-8Edit2)9Edit)+10Edit2+(10Edit-9Edit2-8Edit2)2)
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Total Surface Area of Frustum of Cone given Slant Height, Height and Top Radius Solution

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

FIRST Step Consider the formula
TSA=π(((2rTop-hSlant2-h2)hSlant)+rTop2+(rTop-hSlant2-h2)2)
Next Step Substitute values of Variables
TSA=π(((210m-9m2-8m2)9m)+10m2+(10m-9m2-8m2)2)
Next Step Substitute values of Constants
TSA=3.1416(((210m-9m2-8m2)9m)+10m2+(10m-9m2-8m2)2)
Next Step Prepare to Evaluate
TSA=3.1416(((210-92-82)9)+102+(10-92-82)2)
Next Step Evaluate
TSA=871.571851516107
LAST Step Rounding Answer
TSA=871.5719

Total Surface Area of Frustum of Cone given Slant Height, Height and Top 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:
Note: Value should be greater than 0.
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: rTop
Measurement: LengthUnit: m
Note: Value should be greater than 0.
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: hSlant
Measurement: LengthUnit: m
Note: Value should be greater than 0.
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.
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(ATopπ+ABaseπ)hSlant)+ATop+ABase
​Go Total Surface Area of Frustum of Cone given Slant Height, Height and Base Area
TSA=π(((hSlant2-h2+2ABaseπ)hSlant)+(hSlant2-h2+ABaseπ)2)+ABase
​Go Total Surface Area of Frustum of Cone given Slant Height, Height and Base Radius
TSA=π(((hSlant2-h2+2rBase)hSlant)+(hSlant2-h2+rBase)2+rBase2)
​Go Total Surface Area of Frustum of Cone given Slant Height, Height and Top Area
TSA=π(((2ATopπ-hSlant2-h2)hSlant)+(ATopπ-hSlant2-h2)2)+ATop

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

Total Surface Area of Frustum of Cone given Slant Height, Height and Top Radius evaluator uses 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) to evaluate the Total Surface Area of Frustum of Cone, The Total Surface Area of Frustum of Cone given Slant Height, Height and Top 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, top radius and height 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 Top Radius using this online evaluator? To use this online evaluator for Total Surface Area of Frustum of Cone given Slant Height, Height and Top Radius, enter Top Radius of Frustum of Cone (rTop), Slant Height of Frustum of Cone (hSlant) & Height of Frustum of Cone (h) and hit the calculate button.

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

What is the formula to find Total Surface Area of Frustum of Cone given Slant Height, Height and Top Radius?
The formula of Total Surface Area of Frustum of Cone given Slant Height, Height and Top Radius is expressed as 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). Here is an example- 871.5719 = pi*(((2*10-sqrt(9^2-8^2))*9)+10^2+(10-sqrt(9^2-8^2))^2).
How to calculate Total Surface Area of Frustum of Cone given Slant Height, Height and Top Radius?
With Top Radius of Frustum of Cone (rTop), Slant Height of Frustum of Cone (hSlant) & Height of Frustum of Cone (h) we can find Total Surface Area of Frustum of Cone given Slant Height, Height and Top Radius using the formula - 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). 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 ConeOpenImg
  • 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 ConeOpenImg
  • 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)OpenImg
Can the Total Surface Area of Frustum of Cone given Slant Height, Height and Top Radius be negative?
No, the Total Surface Area of Frustum of Cone given Slant Height, Height and Top 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 Top Radius?
Total Surface Area of Frustum of Cone given Slant Height, Height and Top 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 Top Radius can be measured.
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