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Volume of Frustum of Cone is the quantity of three-dimensional space enclosed by the entire surface of the Frustum of the Cone. Check FAQs
V=13πh((hSlant2-h2+rBase)2+rBase2+((hSlant2-h2+rBase)rBase))
V - Volume of Frustum of Cone?h - Height of Frustum of Cone?hSlant - Slant Height of Frustum of Cone?rBase - Base Radius of Frustum of Cone?π - Archimedes' constant?

Volume of Frustum of Cone given Slant Height, Height and Base Radius Example

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Here is how the Volume of Frustum of Cone given Slant Height, Height and Base Radius equation looks like with Values.

Here is how the Volume of Frustum of Cone given Slant Height, Height and Base Radius equation looks like with Units.

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

1288.8621Edit=133.14168Edit((9Edit2-8Edit2+5Edit)2+5Edit2+((9Edit2-8Edit2+5Edit)5Edit))
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Volume of Frustum of Cone given Slant Height, Height and Base Radius Solution

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

FIRST Step Consider the formula
V=13πh((hSlant2-h2+rBase)2+rBase2+((hSlant2-h2+rBase)rBase))
Next Step Substitute values of Variables
V=13π8m((9m2-8m2+5m)2+5m2+((9m2-8m2+5m)5m))
Next Step Substitute values of Constants
V=133.14168m((9m2-8m2+5m)2+5m2+((9m2-8m2+5m)5m))
Next Step Prepare to Evaluate
V=133.14168((92-82+5)2+52+((92-82+5)5))
Next Step Evaluate
V=1288.8621314173
LAST Step Rounding Answer
V=1288.8621

Volume of Frustum of Cone given Slant Height, Height and Base Radius Formula Elements

Variables
Constants
Functions
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.
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.
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.
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 Volume of Frustum of Cone

​Go Volume of Frustum of Cone given Slant Height and Base Area
V=πhSlant2-(rTop-ABaseπ)23(rTop2+ABaseπ+(rTopABaseπ))
​Go Volume of Frustum of Cone given Slant Height, Base Area and Top Area
V=πhSlant2-(ATopπ-ABaseπ)23(ATopπ+ABaseπ+(ATopπABaseπ))
​Go Volume of Frustum of Cone given Slant Height and Top Area
V=πhSlant2-(ATopπ-rBase)23(ATopπ+rBase2+(ATopπrBase))
​Go Volume of Frustum of Cone given Top Area
V=13πh(ATopπ+rBase2+(ATopπrBase))

How to Evaluate Volume of Frustum of Cone given Slant Height, Height and Base Radius?

Volume of Frustum of Cone given Slant Height, Height and Base Radius evaluator uses Volume of Frustum of Cone = 1/3*pi*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+((sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)+Base Radius of Frustum of Cone)*Base Radius of Frustum of Cone)) to evaluate the Volume of Frustum of Cone, The Volume of Frustum of Cone given Slant Height, Height and Base Radius formula is defined as the quantity of three dimensional space enclosed by the entire surface of Frustum of Cone, calculated using the slant height, height and base radius of the Frustum of Cone. Volume of Frustum of Cone is denoted by V symbol.

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

FAQs on Volume of Frustum of Cone given Slant Height, Height and Base Radius

What is the formula to find Volume of Frustum of Cone given Slant Height, Height and Base Radius?
The formula of Volume of Frustum of Cone given Slant Height, Height and Base Radius is expressed as Volume of Frustum of Cone = 1/3*pi*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+((sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)+Base Radius of Frustum of Cone)*Base Radius of Frustum of Cone)). Here is an example- 1288.862 = 1/3*pi*8*((sqrt(9^2-8^2)+5)^2+5^2+((sqrt(9^2-8^2)+5)*5)).
How to calculate Volume of Frustum of Cone given Slant Height, Height and Base Radius?
With Height of Frustum of Cone (h), Slant Height of Frustum of Cone (hSlant) & Base Radius of Frustum of Cone (rBase) we can find Volume of Frustum of Cone given Slant Height, Height and Base Radius using the formula - Volume of Frustum of Cone = 1/3*pi*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+((sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)+Base Radius of Frustum of Cone)*Base Radius of Frustum of Cone)). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).
What are the other ways to Calculate Volume of Frustum of Cone?
Here are the different ways to Calculate Volume of Frustum of Cone-
  • Volume of Frustum of Cone=(pi*sqrt(Slant Height of Frustum of Cone^2-(Top Radius of Frustum of Cone-sqrt(Base Area of Frustum of Cone/pi))^2))/3*(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)))OpenImg
  • Volume of Frustum of Cone=(pi*sqrt(Slant Height of Frustum of Cone^2-(sqrt(Top Area of Frustum of Cone/pi)-sqrt(Base Area of Frustum of Cone/pi))^2))/3*(Top Area of Frustum of Cone/pi+Base Area of Frustum of Cone/pi+(sqrt(Top Area of Frustum of Cone/pi)*sqrt(Base Area of Frustum of Cone/pi)))OpenImg
  • Volume of Frustum of Cone=(pi*sqrt(Slant Height of Frustum of Cone^2-(sqrt(Top Area of Frustum of Cone/pi)-Base Radius of Frustum of Cone)^2))/3*(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))OpenImg
Can the Volume of Frustum of Cone given Slant Height, Height and Base Radius be negative?
No, the Volume of Frustum of Cone given Slant Height, Height and Base Radius, measured in Volume cannot be negative.
Which unit is used to measure Volume of Frustum of Cone given Slant Height, Height and Base Radius?
Volume of Frustum of Cone given Slant Height, Height and Base Radius is usually measured using the Cubic Meter[m³] for Volume. Cubic Centimeter[m³], Cubic Millimeter[m³], Liter[m³] are the few other units in which Volume of Frustum of Cone given Slant Height, Height and Base Radius can be measured.
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