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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. Check FAQs
hSlant=(3Vπ(ATopπ+rBase2+(ATopπrBase)))2+(ATopπ-rBase)2
hSlant - Slant Height of Frustum of Cone?V - Volume of Frustum of Cone?ATop - Top Area of Frustum of Cone?rBase - Base Radius of Frustum of Cone?π - Archimedes' constant?

Slant Height of Frustum of Cone given Volume and Top Area Example

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Here is how the Slant Height of Frustum of Cone given Volume and Top Area equation looks like with Values.

Here is how the Slant Height of Frustum of Cone given Volume and Top Area equation looks like with Units.

Here is how the Slant Height of Frustum of Cone given Volume and Top Area equation looks like.

9.5851Edit=(31500Edit3.1416(315Edit3.1416+5Edit2+(315Edit3.14165Edit)))2+(315Edit3.1416-5Edit)2
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Slant Height of Frustum of Cone given Volume and Top Area Solution

Follow our step by step solution on how to calculate Slant Height of Frustum of Cone given Volume and Top Area?

FIRST Step Consider the formula
hSlant=(3Vπ(ATopπ+rBase2+(ATopπrBase)))2+(ATopπ-rBase)2
Next Step Substitute values of Variables
hSlant=(31500π(315π+5m2+(315π5m)))2+(315π-5m)2
Next Step Substitute values of Constants
hSlant=(315003.1416(3153.1416+5m2+(3153.14165m)))2+(3153.1416-5m)2
Next Step Prepare to Evaluate
hSlant=(315003.1416(3153.1416+52+(3153.14165)))2+(3153.1416-5)2
Next Step Evaluate
hSlant=9.58512290674049m
LAST Step Rounding Answer
hSlant=9.5851m

Slant Height of Frustum of Cone given Volume and Top Area Formula Elements

Variables
Constants
Functions
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.
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:
Note: Value should be greater than 0.
Top Area of Frustum of Cone
Top Area of Frustum of Cone is the total amount of two-dimensional space occupied by the top face of the Frustum of the Cone.
Symbol: ATop
Measurement: AreaUnit:
Note: Value should be greater than 0.
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: rBase
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 Slant Height of Frustum of Cone

​Go Slant Height of Frustum of Cone given Base Area
hSlant=h2+(rTop-ABaseπ)2
​Go Slant Height of Frustum of Cone given Base Area and Top Area
hSlant=h2+(ATopπ-ABaseπ)2
​Go Slant Height of Frustum of Cone given Top Area
hSlant=h2+(ATopπ-rBase)2
​Go Slant Height of Frustum of Cone given Curved Surface Area and Base Area
hSlant=CSAπ(rTop+ABaseπ)

How to Evaluate Slant Height of Frustum of Cone given Volume and Top Area?

Slant Height of Frustum of Cone given Volume and Top Area evaluator uses Slant Height of Frustum of Cone = sqrt(((3*Volume of Frustum of Cone)/(pi*(Top Area of Frustum of Cone/pi+Base Radius of Frustum of Cone^2+(sqrt(Top Area of Frustum of Cone/pi)*Base Radius of Frustum of Cone))))^2+(sqrt(Top Area of Frustum of Cone/pi)-Base Radius of Frustum of Cone)^2) to evaluate the Slant Height of Frustum of Cone, The Slant Height of Frustum of Cone given Volume and Top Area formula is defined as the length of the line segment joining the extremities of two parallel radii, drawn in the same direction of the two circular bases of Frustum of Cone, calculated using volume, base radius and top area of Frustum of Cone. Slant Height of Frustum of Cone is denoted by hSlant symbol.

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

FAQs on Slant Height of Frustum of Cone given Volume and Top Area

What is the formula to find Slant Height of Frustum of Cone given Volume and Top Area?
The formula of Slant Height of Frustum of Cone given Volume and Top Area is expressed as Slant Height of Frustum of Cone = sqrt(((3*Volume of Frustum of Cone)/(pi*(Top Area of Frustum of Cone/pi+Base Radius of Frustum of Cone^2+(sqrt(Top Area of Frustum of Cone/pi)*Base Radius of Frustum of Cone))))^2+(sqrt(Top Area of Frustum of Cone/pi)-Base Radius of Frustum of Cone)^2). Here is an example- 9.585123 = sqrt(((3*1500)/(pi*(315/pi+5^2+(sqrt(315/pi)*5))))^2+(sqrt(315/pi)-5)^2).
How to calculate Slant Height of Frustum of Cone given Volume and Top Area?
With Volume of Frustum of Cone (V), Top Area of Frustum of Cone (ATop) & Base Radius of Frustum of Cone (rBase) we can find Slant Height of Frustum of Cone given Volume and Top Area using the formula - Slant Height of Frustum of Cone = sqrt(((3*Volume of Frustum of Cone)/(pi*(Top Area of Frustum of Cone/pi+Base Radius of Frustum of Cone^2+(sqrt(Top Area of Frustum of Cone/pi)*Base Radius of Frustum of Cone))))^2+(sqrt(Top Area of Frustum of Cone/pi)-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 Slant Height of Frustum of Cone?
Here are the different ways to Calculate Slant Height of Frustum of Cone-
  • Slant Height of Frustum of Cone=sqrt(Height of Frustum of Cone^2+(Top Radius of Frustum of Cone-sqrt(Base Area of Frustum of Cone/pi))^2)OpenImg
  • Slant Height of Frustum of Cone=sqrt(Height of Frustum of Cone^2+(sqrt(Top Area of Frustum of Cone/pi)-sqrt(Base Area of Frustum of Cone/pi))^2)OpenImg
  • Slant Height of Frustum of Cone=sqrt(Height of Frustum of Cone^2+(sqrt(Top Area of Frustum of Cone/pi)-Base Radius of Frustum of Cone)^2)OpenImg
Can the Slant Height of Frustum of Cone given Volume and Top Area be negative?
No, the Slant Height of Frustum of Cone given Volume and Top Area, measured in Length cannot be negative.
Which unit is used to measure Slant Height of Frustum of Cone given Volume and Top Area?
Slant Height of Frustum of Cone given Volume and Top Area is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Slant Height of Frustum of Cone given Volume and Top Area can be measured.
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