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Curved Surface Area of Frustum of Cone given Volume Formula

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GoCurved Surface Area of Frustum of Cone given Slant Height Formula

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Curved Surface Area of Frustum of Cone is the quantity of plane enclosed by curved surfaces (that is, top and bottom faces are excluded) of the Frustum of the Cone. Check FAQs

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

CSA - Curved Surface Area of Frustum of Cone?r_Top - Top Radius of Frustum of Cone?r_Base - Base Radius of Frustum of Cone?V - Volume of Frustum of Cone?π - Archimedes' constant?

Curved Surface Area of Frustum of Cone given Volume Example

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

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

Here is how the Curved Surface Area of Frustum of Cone given Volume equation looks like.

451.9868 = 3.1416 \cdot (10 + 5) \cdot \sqrt{{(\frac{3 \cdot 1500}{3.1416 \cdot (10^{2} + 5^{2} + (10 \cdot 5))})}^{2} + {(10 - 5)}^{2}}

451.9868m² = 3.1416 \cdot (10m + 5m) \cdot \sqrt{{(\frac{3 \cdot 1500m³}{3.1416 \cdot ({10m}^{2} + {5m}^{2} + (10m \cdot 5m))})}^{2} + {(10m - 5m)}^{2}}

451.9868 = 3.1416 \cdot (10 + 5) \cdot \sqrt{{(\frac{3 \cdot 1500}{3.1416 \cdot (10^{2} + 5^{2} + (10 \cdot 5))})}^{2} + {(10 - 5)}^{2}}

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Curved Surface Area of Frustum of Cone given Volume Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

CSA = π \cdot (10m + 5m) \cdot \sqrt{{(\frac{3 \cdot 1500m³}{π \cdot ({10m}^{2} + {5m}^{2} + (10m \cdot 5m))})}^{2} + {(10m - 5m)}^{2}}

Next Step Substitute values of Constants

∴

CSA = 3.1416 \cdot (10m + 5m) \cdot \sqrt{{(\frac{3 \cdot 1500m³}{3.1416 \cdot ({10m}^{2} + {5m}^{2} + (10m \cdot 5m))})}^{2} + {(10m - 5m)}^{2}}

Next Step Prepare to Evaluate

∴

CSA = 3.1416 \cdot (10 + 5) \cdot \sqrt{{(\frac{3 \cdot 1500}{3.1416 \cdot (10^{2} + 5^{2} + (10 \cdot 5))})}^{2} + {(10 - 5)}^{2}}

Next Step Evaluate

∴

CSA = 451.986764142723m²

LAST Step Rounding Answer

∴

CSA = 451.9868m²

Curved Surface Area of Frustum of Cone given Volume Formula Elements

Variables

Constants

Functions

Curved Surface Area of Frustum of Cone

Curved Surface Area of Frustum of Cone is the quantity of plane enclosed by curved surfaces (that is, top and bottom faces are excluded) of the Frustum of the Cone.

Symbol: CSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Curved 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 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

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 Curved Surface Area of Frustum of Cone

Go Curved Surface Area of Frustum of Cone

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

Go Curved Surface Area of Frustum of Cone given Slant Height

CSA = π \cdot (r Top + r Base) \cdot h Slant

Go Curved Surface Area of Frustum of Cone given Total Surface Area

CSA = TSA - (π \cdot ({r Top}^{2} + {r Base}^{2}))

Other formulas in Curved Surface Area of Frustum of Cone category

Go Base Area of Frustum of Cone

A Base = π \cdot {r Base}^{2}

Go Top Area of Frustum of Cone

A Top = π \cdot {r Top}^{2}

Go Total Surface Area of Frustum of Cone given Slant Height

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

Go Total Surface Area of Frustum of Cone

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

How to Evaluate Curved Surface Area of Frustum of Cone given Volume?

Curved Surface Area of Frustum of Cone given Volume evaluator uses Curved Surface Area of Frustum of Cone = pi*(Top Radius of Frustum of Cone+Base Radius of Frustum of Cone)*sqrt(((3*Volume of Frustum of Cone)/(pi*(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone*Base Radius of Frustum of Cone))))^2+(Top Radius of Frustum of Cone-Base Radius of Frustum of Cone)^2) to evaluate the Curved Surface Area of Frustum of Cone, The Curved Surface Area of Frustum of Cone given Volume formula is defined as the quantity of plane enclosed by curved surfaces (that is, top and bottom faces are excluded) of the Frustum of Cone, calculated using the volume, top radius and base radius of the Frustum of Cone. Curved Surface Area of Frustum of Cone is denoted by CSA symbol.

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

FAQs on Curved Surface Area of Frustum of Cone given Volume

What is the formula to find Curved Surface Area of Frustum of Cone given Volume?

The formula of Curved Surface Area of Frustum of Cone given Volume is expressed as Curved Surface Area of Frustum of Cone = pi*(Top Radius of Frustum of Cone+Base Radius of Frustum of Cone)*sqrt(((3*Volume of Frustum of Cone)/(pi*(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone*Base Radius of Frustum of Cone))))^2+(Top Radius of Frustum of Cone-Base Radius of Frustum of Cone)^2). Here is an example- 451.9868 = pi*(10+5)*sqrt(((3*1500)/(pi*(10^2+5^2+(10*5))))^2+(10-5)^2).

How to calculate Curved Surface Area of Frustum of Cone given Volume?

With Top Radius of Frustum of Cone (r_Top), Base Radius of Frustum of Cone (r_Base) & Volume of Frustum of Cone (V) we can find Curved Surface Area of Frustum of Cone given Volume using the formula - Curved Surface Area of Frustum of Cone = pi*(Top Radius of Frustum of Cone+Base Radius of Frustum of Cone)*sqrt(((3*Volume of Frustum of Cone)/(pi*(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone*Base Radius of Frustum of Cone))))^2+(Top Radius of Frustum of Cone-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 Curved Surface Area of Frustum of Cone?

Here are the different ways to Calculate Curved Surface Area of Frustum of Cone-

Curved Surface Area of Frustum of Cone=pi*(Top Radius of Frustum of Cone+Base Radius of Frustum of Cone)*sqrt((Top Radius of Frustum of Cone-Base Radius of Frustum of Cone)^2+Height of Frustum of Cone^2)
Curved Surface Area of Frustum of Cone=pi*(Top Radius of Frustum of Cone+Base Radius of Frustum of Cone)*Slant Height of Frustum of Cone
Curved Surface Area of Frustum of Cone=Total Surface Area of Frustum of Cone-(pi*(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2))

Can the Curved Surface Area of Frustum of Cone given Volume be negative?

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

Which unit is used to measure Curved Surface Area of Frustum of Cone given Volume?

Curved Surface Area of Frustum of Cone given Volume 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 Curved Surface Area of Frustum of Cone given Volume can be measured.

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Curved Surface Area of Frustum of Cone given Volume Formula

​GoCurved Surface Area of Frustum of Cone Formula

​GoCurved Surface Area of Frustum of Cone given Slant Height Formula

Curved Surface Area of Frustum of Cone given Volume Example

Curved Surface Area of Frustum of Cone given Volume Solution

Curved Surface Area of Frustum of Cone given Volume Formula Elements

Other Formulas to find Curved Surface Area of Frustum of Cone

Other formulas in Curved Surface Area of Frustum of Cone category

How to Evaluate Curved Surface Area of Frustum of Cone given Volume?

FAQs on Curved Surface Area of Frustum of Cone given Volume

Variable Name

GoCurved Surface Area of Frustum of Cone Formula

GoCurved Surface Area of Frustum of Cone given Slant Height Formula